David Cameron's decision to veto an EU-wide treaty change over eurozone rules was "largely political", Business Secretary Vince Cable has said.
Mr Cable told the BBC the prime minister "got a short-term boost from it, but it doesn't actually deal with the big long-term problems in Europe".
But Boris Johnson backed the veto and warned against "hysterical attempts to bubblegum" the eurozone together.
The London mayor predicted Greece would leave the eurozone within a year.
"I would be amazed if we were all sitting here next year and the euro had not undergone some sort of change," Mr Johnson told BBC One's Andrew Marr Show.
"I think it highly likely that there will be a realignment in the sense that some countries will fall out... and we all know who the likely candidates are," he said, adding that ouzo (a Greek drink) would be "substantially cheaper" in a year's time.
"But there is such phobia about this and such a lot of political ego has been invested in the success of the euro project that people are failing to see that might be the best way forward."
Mr Johnson - described on the programme by Labour's Lord Mandelson as Mr Cameron's worst nightmare - also said he saw no reason for an immediate referendum on UK membership of the EU.
During his appearance on the same programme, Mr Cable agreed with the suggestion that the use of the British veto had not put the UK's financial sector in a stronger position.
Asked if he had thought about quitting in the wake of EU veto, Mr Cable said "No", before adding: "I frequently wonder about my position in government because we're all making difficult decisions.
"But when I reflect on it as I do, I realise that what we're committed to is actually making this government work; we've got to deal with the very serious problems in the economy."
'A bit of red meat'
Mr Cable said there were lots of differences between the coalition partners but the focus was on sorting out the UK's economy while also putting some Lib Dem policies into action, such as with the forthcoming plans to reform the banks.
Mr Cable later told BBC Radio 4's The World This Weekend that it would take time to judge the consequences - "whether it has done good or done harm" - of the British veto.
He also said he thought the European Union had been a "bulwark" against 1930s-style moves towards nationalism and protectionist policies.
Lib Dem leader, and deputy prime minister, Nick Clegg told Sky News that there was a clear understanding across government that it was in the UK's interests for the euro to survive, saying that 3m British jobs depended on EU membership.
He said: "I read and hear a lot of people breezily predicting, almost with a sense of glee, that the eurozone is going to fall apart and this country is going to drop out of the euro.
"My crystal ball is no clearer than anybody else's - what I do know is that no-one should lightly wish for that outcome.
"We need to try to move from a phase of uncertainty to a phase of greater stability and I don't think witnessing the break-up of the currency bloc on our backyard would do us any good at all."
Former Labour cabinet minister Lord Mandelson, who is also a former European Commissioner, told the BBC that the proposed EU treaty change had not posed any "threat to Britain whatsoever".
He described the PM's actions as "whipping up a bit of storm, a bit of red meat to throw to Mr Cameron's anti-European backbenchers".
Following Friday's increasingly outspoken comments about the British economy by senior figures in France, Mr Clegg repeated his view that the countries were "stronger when we work together".
He said that there were often instances of "tit-for-tat" verbal rows between the UK and France through history, but the two countries "always do better when we pull in the same direction".