Then you realise that it does - no-one is quite sure how this will play out. Either there will be an effort to go for the Prime Minister if Labour loses the Glenrothes by-election in Fife (probably next month) or - much more likely - the approach of the local and European elections next summer will precipitate the crisis. That's a sombre prospect for ministers, but it's one they all seem to share.

Politics always operates in two dimensions at once, the public and the private. But talking to a cross-section of the Cabinet here, on the conference round - hearing what they'd only say in private - you realise how different the public displays of unity are from the anxiety underneath.

"It's hell," one of them said last night. Another put it like this: "If Gordon can make people feel good about this government in his speech - just happy again - it will be fine. If not, we've got a long fight on our hands."

That came from a strong supporter of the Prime Minister. All of them speak of a Cabinet in which, by a common estimate, there are four ministers who could resign - though no-one thinks they'd do it en masse. And individually none has the making of a Spartacus on the backbenches to lead the mob into battle.

"Just look at them. It's very thin. Not really serious," says one minister about the backbench rebels and the disaffected bit of the Cabinet (not, incidentally, a comment meant to include David Miliband).

Struggling through

Thin, maybe. But you don't have to spend time with many ministers to realise how corrosive this is - a word I heard from three members of the Cabinet last night.

The fear is obvious. Either a move against the Prime Minister next month (in some unspecified way), or a spring coup - unless Gordon Brown can somehow engender a different spirit among his ministers.

Along with "corrosive", a favourite phrase these days is "struggling through". It reflects the feeling that maybe the real danger for them is a simple draining of energy that leaves them all floundering. This Cabinet minister's analysis sums it up: "If Gordon gets the Tory lead under 10% by Easter he'll probably be there for the election. Otherwise, probably not."

Nothing has really happened here in Manchester, rather confusingly. "That speech was neither one thing nor the other" one of his colleagues - and friends - said of David Miliband's performance in the hall.

It was neither a declaration of permanent loyalty nor a signal of burning ambition. The truth is that as things stand there is no alternative leader with a movement behind him. So you might be tempted to think that they all believe a potential crisis has passed.

They do. But they don't think that is a feeling that will last. You'd find it hard to winkle out a Cabinet minister here who believes this is over. Their real difficulty is that they can't read the next chapter, using the ability they treasure so much at the top of politics. So they're troubled, and that won't change with one speech.

It's not infallible. But it usually works. In 2000, for example, there's no doubt that to many voters George Bush seemed less intimidating than the stiff and slightly aloof Al Gore. Now Gore has adopted a loose young-grandfatherly kind of style - he introduced Obama with Stevie Wonder at the football stadium in Denver - and would be rather more palatable. As for the President, the kindest thing to say is that the good guy image has lasted. But it was true at the time.

An authentic appeal

Applying the rule to this year gets you to the heart of it, because you realise why the choice is so difficult for so many people. Both candidates have an authentic appeal - John McCain because there's grit and fascination in his personal history and a slightly cranky unpredictability about him; Barack Obama because he's a phenomenon, eloquent and supremely relaxed despite his celebrity. McCain dispenses wisdom at the soda fountain; Obama because he's the new guy in town, not without a whiff of danger. They both have attached to them an unmistakably American story.

One of the reasons why they've come out of their conventions more or less neck and neck is that for voters who haven't already jumped on board with one or the other, or having party loyalties, each offers something out of the ordinary. McCain's age acts against him; Obama's "otherness" - and that includes his race - has the same effect, but they both have the ability to cast a spell.

This produces a natural tendency to think that they are somehow similar, despite their different histories. Don't be misled by the fact that they're both strong candidates. It's a fallacy to think that because they're running close the choice is less of a choice.

The marathon sprint

After the conventions, they're starting on a two month run to polling day - you might call it a marathon sprint - that will be an argument about political culture perhaps more than on the detailed questions where they disagree (health care, education, tax cuts and privileges). It's true that their policies in office on Iraq, or towards Russia, for example, would be closer than they'd have you believe. Economically they'd face the same limited choices as a consequence of the huge Bush deficit, much more limited than either would like to admit. But the result will set a course for America.

John McCain's selection of the extraordinary Sarah Palin acknowledges that he can't win without that part of the Republican family that is profoundly evangelical, socially conservative and ideologically determined. Her speech was a populist clarion call to people who felt that after the disappointments of the Bush years (they didn't want a deficit, worry about the war, lost heart that the conservative revolution was in the doldrums) they were going to be left out.

Should McCain win, the conservative tide stirred up so brilliantly by Ronald Reagan will gather strength again. You could expect climactic arguments over abortion, and battles over the next Supreme Court justices.

Two may be required over the next few years and the selections will make the difference between a centrist court and one which is either regularly conservative (maybe challenging the landmark Roe v Wade ruling on abortion) or liberal once again, as it was for two generations until the later Reagan years. A McCain presidency would almost certainly be hobbled by a Democratic Congress - he'd probably have to swallow a health care plan Republicans didn't like, and might do it - but it would revive the right.

Obama, on the other hand, would have, almost certainly, a Democratic Senate and House - which Bill Clinton only had for two of his eight years - which would make him the first Democrat for a generation (Jimmy Carter) to have that benefit. Legislatively, he'd be more comfortable than any Democrat since Lyndon Johnson in the 1960s, in the balmy days before Vietnam got him by the vitals. And he would have the power to change the way politics works - maybe even to challenge the socially conservative orthodoxy that's grown up (remember that in the last 40 years, Republican presidents have been in office for 28).

Obama would change the rules, simply because of who and what he is, and by his style. We can't tell just how he would take advantage of a wide window of opportunity that would open for him. That is a story for another day.

The snare of war

Behind the rhetoric, and the boiled down partisan arguments, that's what's most important about this election; and maybe why it matters to many people outside the United States. They may be running in step round the last bend, but they are candidates who promise diverging paths for the next generation. They may even agree on more than they'd care to admit publicly, and the snares of the economy and war would undoubtedly hold them back, but don't doubt it: their presidencies would take America in quite different directions.

That is understood - felt - by the electorate, and that's one of the reasons why voter registration is up, excitement is high and why nearly 40 million people tuned in to hear the two candidates accept their nominations and why - even more remarkably - Sarah Palin got much the same figure. She got the biggest audience in history for a vice-presidential acceptance speech, without question. Think about that, and Obama's rallies. There is something going on that we haven't see before, and probably won't see again for a long time.

I was sandwiched somewhere between the Kansas and Arkansas delegations on the floor of the hall and there was weeping and wailing throughout (and no gnashing of teeth). At the end, people were luxuriating in that strange mixture of relief and exhilaration that comes only after a period of tension, because no-one knew whether she could deliver.

They loved it, as they should have.

It exculpated the feeble George Bush performance on video of the night before - and it reminded them why they are Republicans in their party of today. It reminded me of Norman Tebbit or Michael Heseltine or Tony Benn at their height, lifting a party audience in Blackpool or Brighton to a brief passage of frenzy. The question is: will it last?

Republican organisers around the United States will be thrilled, and rightly so. She'll be a star on the circuit. This weekend she'll be trailed by every camera crew they can find. The shock-jock hosts of Talk Radio, resolutely placed in the right-wing corner, will make her a hero overnight. But that's not the whole story. In the course of her speech - much longer than had been planned for her - she sent forth two big salvos. One was aimed straight at Barack Obama (the man who'd written two memoirs before he'd written a piece of Senate legislation, she said - a very good line) and other against the 'big powerbrokers' who're lumped together with 'the lobbyists' and 'Washington' as the enemy of the people.

It was odd to see be-suited New Yorkers and corporate lawyers - they're everywhere around the convention hall, as they were with the Democrats in Denver - rising to applaud her. Did she know they were there? Of course she did. Rather like the claim, made by both parties, that what's called 'energy independence' is available to Americans in the foreseeable future, it's an easy gesture that doesn't bear too much examination. Indeed, it's rather absurd. A speaker who is preceded by Rudy Giuliani, Mike Huckabee and Mitt Romney promising to dismantle the 'old boys' network' and being cheered, just as they had been cheered one by one a few minutes beforehand, is promising a journey into the surreal.

But, make no mistake, Sarah Palin was very good. She gave this party a feeling that it could still win, which it didn't have in its guts last night. It hadn't sunk into despair, but there was real worry about Obama's performance last week. A clutch of polls putting him over 50% for the first time across the country (however sceptical we should be about these national surveys in the US) and streaking ahead in some toss-up states like Iowa and Minnesota (where we are) added to the concerns.

It was reported this morning that the Republicans have given up television advertising in New Mexico because they think the state has gone already: these are grim tidings at the start of the last act of the election.

Relief

Well, Palin managed to expunge all that, or much of it. It may be a passing victory, but it was a victory for McCain all the same. When he came on stage for a brief appearance, as Obama did last week after his running mate's speech, you could see the relief. The maverick had made the right bet.

So it seems now. She will be a pivotal part of the Republican campaign, but she will have difficulties. On the social agenda, she differs from McCain; they'll be asked to explain their differences, and that will be a challenge. What of global warming, which he thinks is a crisis but many on the right of his party describe as some kind of liberal plot? Can they manage their message on abortion, on gay rights, on immigration? We have only just begun the real policy fight.

That, however, is for next week and beyond. Remember now that the Republicans have rallied. They've effectively sidelined George W Bush, whose presence at this convention has been like that of the embarrassing relative who's soon to be gone, and they've got a candidate and running mate who can tell stories of experience and innocence, and make them seem one.

The Democrats, if they're to trump that, are going to have to work hard. Obama has some magical political gifts and Joe Biden, his running mate, is a street fighter of experience and skill. But the McCain pitch - 'Country before Party' - is strong; and so is the shucks-I'm- an-all-American-hockey-mom style of Palin. To foreign eyes the flag-waving seems ever-more over-the-top (and the references to 'Europe' from the platform and the floor this week have been universally tart; even mocking) and the idea that 'service' can trump any political argument or record is sometimes alarmingly simplistic.

But it matters in this contest. Voters, who've been polled and polled until some of them must be worn out, are assumed to care about authenticity and commitment to the country: everything else is an add-on. That's why the candidates seem so often to be saying the same thing, despite the arguments on both sides that this is a vital choice.

I leave you with one question. Because the polls and the focus groups report that Americans, in general, want more consensus and less poisonous partisanship that is a theme that is repeated again and again on the platform here (John McCain will certainly use it tonight) just as it was in Denver last week.

But during the Sarah Palin speech, if I'd suggested to any of the delegates around me that perhaps what was needed was a little more of what McCain has always championed - less crude party battling and deals 'across the aisle' in Congress - I'd have been in danger of being bashed to an ugly pulp by one of the hospitality umbrellas given here. The same would have been true last week in Denver.

Obeisance is paid to bipartisanship, but the truth is that America's divisions are real, and unhealed. Sarah Palin exploited them very skilfully last night.

She's good news for the Republicans at the moment. But her arrival does mean that this campaign is going to be very rough indeed. That cannot now be avoided, even if they're talking throughout about being nicer to each other. Bipartisan? Pass the smelling salts. This is an election, down to the wire.

Here in Minneapolis, politics has been officially suspended. But, of course, this event has deep political implications. There's no contradiction in this: it's perfectly honourable for John McCain to be personally gripped by the plight of the people in the hurricane's path - "in harm's way" as they say in a cliché that seems to spring up on every page of every speech these days - and at the same time to be giving some thought to the political implications. He would be daft if he didn't.

Similarly, Barack Obama is well aware that this disaster - if that's what it turns out to be - will focus people's minds on the issue of leadership, which is the heart of the presidential election, and so he has to consider how best to play his cards.

The reason why leadership is important is that George W Bush's presidency was hit amidships by Hurricane Katrina, and the political damage was probably as great as that done by Iraq. Many Americans were ashamed at the performance of their government in response to the catastrophe - buses that couldn't get from Atlanta to New Orleans, flood defences that weren't there, the terrible sight of 1,800 people dying in an American city, most of them poor and without anything to help them get out of "harm's way". A very senior figure in the administration told me a year later that it was, in this official's judgement, a series of mistakes that would never be forgotten by the people. The mistakes fell into two categories - the simple bureaucratic bungling that has often dogged this administration, and the apparent fecklessness of the president himself, who was in Arizona (at John McCain's 69th birthday party) when the (predicted) crisis began, and who had to suffer the indignity of his chosen head of the Federal Emergency Management Agency being exposed in subsequent congressional inquiries as hopelessly inadequate and someone who held the post principally because he was an old Bush family crony. The consequence for Mr McCain is profound.

View of New Orleans

He has to demonstrate that he behaves differently. That is why on Sunday he decided to behave like a president-in-waiting. He's got no more locus in the crisis that Barack Obama (except that it's his party convention that Mr Bush has decided not to attend....) but he immediately took to the skies with Gov Sarah Palin, his running mate, and began to speak as if it was he who was directing the operations.

When it all began, the view around the convention here was that it was all bad news for the Republicans. I wasn't entirely sure about that, though it was the first obvious thought, and have become even more convinced in the last few hours that Mr McCain could emerge from this strengthened. It plays to his particular qualities, and fits with the general feeling that he is probably a good man in a crisis. All that leaves Senator Obama on the sidelines, a bit out of it. He's said all the right things - he's staying away because he doesn't want to get in the way, his vast army of supporters will be encouraged to donate money to the clean-up effort if it's required - but it may well be that by the time the week is over, John McCain will have achieved what, for him, has been one of his aims for a long time (and a very tricky one to accomplish) - to make a contrast with the sitting president.

Until Gustav began to loom so menacingly, the talk here had been about the surprise McCain choice of Sarah Palin as running mate. There's no doubt that it's a risk. Her political experience is limited - being a mayor and then a governor in Alaska isn't premier league stuff, however challenging the negotiations with oil companies might be - and no-one can be sure how she will stand up to the day-and-night presence of microphones and cameras by her side for the next 60 days.

But there is one huge plus for McCain. Over the weekend, he raised $7m from social conservatives who were delighted by her appointment. There were reports from the platform committee here that some of its members were weeping with joy when they heard of it (and ascribing mcCain's wisdom to divine intervention, as is their wont); Pastor Jim Dobson - one of the most influential figures on the evangelical Right - says it has finally persuaded him to recommend voting for McCain. Sarah Palin is what's known as a 'movement conservative' - 'sound' on the questions of God, guns and gays and absolutely opposed to abortion. She will be sent out to those who were recruited to the Republican cause by Karl Rove when he was building a new coalition for George Bush. Once again they will be stuffing the envelopes, manning the phone banks. For the Republicans, this is important. They desperately need that base; Obama's army is enormous, and his new registrations among voters are very threatening to McCain. Without 'the base' he'd be sunk. Moreover, he is lagging badly among women voters. Palin - mother of five, classic America mom, wife of an Alaskan fisherman - is reckoned to be a character who will make the ticket more attractive.

But....there is no doubt that it is a gamble. The two don't know each other well. It could backfire. There are plenty fingers crossed among Republicans here.

They know that about 40 million people watched the Obama speech in Denver last week, more Americans than watched the opening of the Olympics. McCain needed something eye-catching, and he found it.

And then came Gustav. Where will this end?

I do not know, but I know this: don't pay any attention to the national opinion polls. They put the candidates neck and neck, but the people I know who're immersed in this stuff - Democrats, Republicans and many in between - don't believe that they're telling us very much. Firstly, it isn't a national vote for president, of course, but a state-by-state contest.

Second, the samples are vanishingly small. I saw a poll the other day purporting to give an accurate picture of the views of a country of more than 300 million with a sample of fewer than 800 voters. I'm sorry, but I want something better than that. It's far better to look at state polls.

This election, and all that hangs on it, is determinedly unpredictable. There used to be a rule of American politics that most voters didn't make up their minds until the end of the baseball World Series, in the third week of October (that is, about two weeks before polling day). That's less true now, but it's worth remembering. Many of them are just tuning in now. Add that to everything we've seen in the last week alone and you realise what lies ahead.

McCain and Obama are locked in a titanic struggle. And today, the Bush presidency - dealing with another hurricane - seems more on the wane than ever. Few presidents have seemed to cede so much power with four months to go before leaving office, but that's what's happened. It's a measure of the quality of this contest, and the seriousness of its arguments. Don't tell me that it isn't a good thing. It is.

One of the peculiarities of American politics in the last few years has been the explosion of comedy and satire - previously not one of its strong points, at least intentionally.

The Daily Show with Jon Stewart, on the Comedy Central cable network, is now in the staple diet of the political classes. Washington treats it almost like the news, and the candidates have to accept invitations to appear, although in doing so they court humiliation.

One of the performers on the show is the British comedy writer John Oliver. I asked him if he was surprised to see American politicians, who traditionally take themselves rather seriously, appearing on a satirical show.

This was his answer: "When they stop to talk to us in the field, there's this weird feeling. You think, why are you doing this, why are you putting yourself through this?

"You know what's going to happen. You know it's going to be humiliating. Do you want to be the leader of the free world this badly? It seems to be the new way of showing how much you want to be president, will you prostitute your dignity for it?

"And the answer is, yes."

Joe Klein on Time magazine said on the Today programme that he still waited for the 'moment of romantic transcendence' and you don't have to be a political junkie to know what he means. How will Bill Clinton conceal his angst, which became such a feature of the late primary season? How will Hillary couch her support? And can Barack Obama himself avoid turning his vast rally on Thursday - in front of 85,000 people in the open air - into an event that scares as many voters as it attracts?

10 weeks

These are all part of the tableau that's being played out for the voters, and some of its impressions will last. Election Day is 10 weeks away (at last, the voters cry) and events in the next two weeks - the Republicans gather in Minneapolis next weekend - will help to shape the impressions of voters who will swing this contest one way or the other. Both parties think it will be close. Frank Luntz, the pollster, goes so far as to say that the first presidential debate (there will be three, as well as one for the running mates) could decide it: a decisive break to the front for one candidate might be enough.

I don't go along with that entirely, simply because I think that it's more likely that there will be back-and-forth swings in the coming weeks, probably engendered by events from outside of which at the moment we can know nothing. There's also the matter of John McCain's temper (famously unpredictable) and Barack Obama's tendency to lose his platform fluency when he's engaged in debate. All we know is that it will swing to and fro before it's over.

So will the convention itself. You can be sure that lurid rumours will surface, I would guess within 12 hours of his arrival, about Bill Clinton's disposition, only to disappear a few hours later. The web will be awash with gossip and trivia, and some of it will have a brief moment of life before evaporating and being forgotten. I heard George Stephanopolous of ABC News (and the Clinton White House) talking today about how journalism in this atmosphere is becoming more and more a matter of raw editing. How much of this stuff do you believe? When do you run with a story and when do you let it drop? There are no editors on the web, and hordes of characters - some well-informed and some ignorant, some malicious and some serious - who're pouring out 'information' which is often a messy mixture of fact and prejudice, emotion and rational argument. It's hard to dissect.

The consequence is that the atmosphere is fevered. Stories circulate and fall away within a couple of hours. There used to be the notion of a 'news cycle' that could be manipulated by a campaign in timing an announcement and letting it run. That has gone (and a good thing too) but it has been replaced by an anarchic torrent that certainly gives us all more information, but often muddles truth and falsehood and elevates the nonsensical into something substantial, if only for a moment.

So it will be a merry-go-round. I'm struck already by the Democrats' state of mind. They're enthusiastic about Obama, who'll play a hero's role this week, but they have a lurking feeling that he needs to find another gear. They think John McCain will run into trouble - his campaign history suggests it - but they're well aware of his formidable appeal as a man of valour and independence of mind, and - most worrying of all for them - his ability in debate. Obama will be a nervous man (though he never looks it) as he walks onto that stage for the first of them, next month.

All that lies ahead. First, there is the business of the nomination itself, complete with the roll-call vote as a gesture to Hillary, to ease the pain; the speeches from Bill, Jimmy Carter, Al Gore, even John Kerry (who shouted 'fantastic' at me today when I asked him to describe the coming week - hardly a usable quote).

There will be daft moments, and no doubt a couple of speeches that bomb. The one that may surprise people, I suspect, is Joe Biden's vice-presidential acceptance speech on Wednesday. He's long since given up using lines from Neil Kinnock speeches, the rather charming offence that scuppered his short presidential run in 1988. He's gritty, tough, and - that word Americans so treasure - authentic.

That's how it feels as Denver waits. There's an intriguing historical parallel. The last Democrat convention to be held here was in 1908, exactly a century ago. President Teddy Roosevelt had gone, having given the progressive Republican cause much to cheer about, and to win back the White House the Democrats nominated William Jennings Bryan, the great populist whose campaigns against the growing corporations was so popular. But, for the third time, he lost and put Robert Taft - an isolationist - in the White House.

Fortunately for them, few of the Democrats who're settling down for a week of celebration and partying are worrying about history. Just as well. But I bet that Barack Obama knows it backwards. He knows how fragile his grip on popularity may be; his job is to tighten his grip. Michelle, his wife, starts the job in the Convention Hall. The real question is: Americans may admire it, but how many will like it? That's the calculation that begins in earnest here today.