Theresa May could quit as Tory leader on Thursday if MPs vote for a new backbench Brexit deal on Wednesday.
But the PM will make another attempt on Tuesday to get her Brexit deal through Parliament – as Cabinet ministers pressurise her to call a General Election if she fails.
A Number 10 source said: “This is it. This really is the last chance saloon.”
Mrs May’s deal was rejected for the third time by 58 votes on Friday and most ministers fear it is now dead.
On Monday - April 1 - Tory grandee Sir Oliver Letwin – described by Tory wags as “leader of the provisional government” – will bring forward another set of proposals for MPs to vote on.
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Favourite to succeed is former Cabinet minister Ken Clarke’s plan for a customs union, which lost by only eight votes last week.
If enough MPs vote for it on Monday then the process to put it into legislation will begin on Wednesday – but Mrs May is unlikely to be the PM to negotiate it. A Cabinet minister told the Sunday Mirror: “If there was legislation it would have to go through both the Commons and the Lords.
“The prime minister would have to negotiate it but that means the office, not the person. So it would depend on who the PM was at the time.”
Whitehall sources were adamant Mrs May will do whatever Parliament instructs her.
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One said: “It might be difficult for her, but it is not impossible.”
Tory Nick Boles, who proposed a single market solution, said if Mrs May was not happy to accept Parliament’s mandate her deputy David Lidiongton or Environment Secretary Michael Gove could do the job.
But many Tories are convinced Mrs May will have to go once it becomes clear we are to hold EU elections.
Nigel Evans of the Tory backbench 1922 Committee said: “If there’s to be a long extension then she might as well be packing her bags.”
Another senior Tory said: “Mrs May can’t negotiate this, which is why she will have to go early.”
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Labour ’s Kevan Jones added: “She has always been the problem and she should go now.”
Jeremy Corbyn waded in by calling for Mrs May to quit and let the “sensible people take over”.
He told a rally: “The priority is to end this chaos the Government has brought us to by running down the clock and bullying and threatening people. The bullying hasn’t worked, the threats haven’t worked. It’s time for the sensible people to take over.”
Speaking in Wales ahead of next week’s Newport West by-election triggered by the death of Labour MP Paul Flynn, Mr Corbyn warned the country was in “a very dangerous period”.
Cabinet ministers are urging the PM to thwart Mr Clarke’s customs union plan by attaching a confidence motion to Tuesday’s vote. That could force an election.
Parliament would then be dissolved before Mr Clarke’s plan could begin its legislative progress. The PM would put her deal to the people and we’d troop to the polls on May 23, the same day as EU elections.
Most Tory MPs say it would be madness for Mrs May to lead them into another election and this is a Cabinet attempt to blackmail them into voting for the PM’s deal.
But Shadow International Trade Secretary Barry Gardiner said: “I’d welcome a snap General Election.”
Labour’s Hilary Benn, chair of the Commons Brexit committee, said: “There is no way this can be sorted by April 12. There has to be a long extension for new negotiations.”
