For the Guardian, it is the most important week of Mrs May's premiership, but the paper says there are few signs of the shift in opinion she had hoped for before Christmas, when she postponed the vote on her Brexit deal.
The Metro predicts the prime minister could face the biggest defeat ever suffered by a government, while the Daily Mirror says simply that she could be gone "within days".
"The Plotters Break Cover" runs a headline in the Daily Mail, which carries profiles of what it calls a "motley crew" of Tory MPs who it accuses of conspiring to seize power from the prime minister.
But reports of a plot are greeted with scepticism in the Financial Times.
A Eurosceptic Tory MP tells the paper the story seems "very helpful to Number 10" and people are taking it "with a pinch of salt".
The Guardian reports that the EU is preparing to offer Mrs May a delay to Brexit - at least until July - if she fails to get her withdrawal agreement through the Commons.
The Times says Brussels is also expected to give written assurances on the Irish backstop, through an exchange of letters today, but the move is thought to be unlikely to make any difference to the vote.
The Brexiteer MP, Mark Francois, is quoted by the Financial Times as saying that Brussels would make a series of "apparent concessions", but they would be "legally meaningless".
Clean air strategy
According to the Times, the government's new clean air strategy contains measures that could eventually cut the costs of air pollution to the NHS and the economy by £1.7bn a year.
The Guardian says the plans go beyond existing EU rules and, for the first time, farmers will come under the new regulations.
But campaigners tell the Financial Times the strategy ducks the question of how ministers intend to meet existing air quality targets, which have been missed repeatedly in the past.
The Daily Telegraph urges the government to adopt a new approach in the case of the jailed British-Iranian woman, Nazanin Zaghari-Ratcliffe, who is due to begin a three-day hunger strike.
In an editorial, the paper argues that the affair has not been handled well by the Foreign Office.
The least that can be done now, the paper says, is to raise the stakes by affording Mrs Zaghari-Ratcliffe diplomatic protection "before an injustice becomes a tragedy".
News that the Royal College of Physicians is to ask its members for their views on assisted dying leads the Daily Mirror.
Next month, 35,000 hospital doctors will be asked whether they think the practice should become legal and, if so, whether they would be prepared to actively participate in assisted dying.
The campaign group, Dignity in Dying, welcomed the poll.
But Prof Patrick Pullicino, of East Kent Hospitals NHS Trust, tells the Mail assisted dying is just "the thin edge of the wedge".
Finally, the Sun reports that sloppy errors have been found to blight the vast majority of CVs.
According to the paper, a review of 20,000 CVs submitted online found that nine in 10 of them contained at least one spelling mistake, or blunders such as rogue apostrophes.
Among the most commonly mis-spelled words were "experience" and "liaising".
Eighteen to 24-year-olds are singled out as the worst offenders.
But, according to the Telegraph, there are some grounds for hope.
Women were twice as likely to check for mistakes as men.
And some parts of the country fared better than others, with the most accurate CVs submitted by job hunters in Yorkshire.