Political sources have claimed a vote of confidence could be forced through by lunchtime on Thursday as the prime minister faces a fierce backlash from both sides of the Brexit divide.
Mrs May cleared the first hurdle when Cabinet ministers finally approved the draft terms of her EU withdrawal agreement at a stormy five-hour meeting on Wednesday.
But she now faces a battle to get it through Parliament as Brexiteer Conservative MPs - as well as some Remainers - condemned the plan, accusing her of breaking promises and handing control back to Brussels.
The BBC’s political editor Laura Kuenssberg reported: “One senior Tory told me tonight there is likely to be a move against the prime minister in the next 24 hours.
“Another said they would be amazed if enough objections to start a contest hadn't emerged by lunchtime.”
She added that this could be “the moment the Tory party falls into a leadership contest almost by mistake”.
Rumours continue at Westminster that the tally of Conservative MPs who have submitted letters of no confidence in Mrs May is about to reach the 48 threshold needed to trigger a vote on her position.
ITV political editor Robert Peston also fuelled rumours that a vote of no confidence was imminent, claiming a source told him there would be enough letters to force one “by lunch” on Thursday.
“Tory Brexiters become angrier and angrier as they wade through 585 pages of the Withdrawal Agreement,” he wrote.
“They tell me there will be enough letters in with Brady of [the committee] by lunch tomorrow to force vote of confidence!”
Nicola Sturgeon, appearing on Peston’s show on Wednesday night, said she “wouldn’t put money” on Mrs May still being prime minister on March 29, the day the UK is due to formally leave the EU.
She said: “The prime minister has proved to be resilient over the last month so you know let’s not count her out in that respect.
“I thought, and remember I’m doing this interview just after she’s made her statement, all sorts of things could have changed, but I thought her language about the collective decision of the Cabinet not a unanimous decision said something, I thought her body language looked very shaky and I wouldn’t rule out cabinet resignations tonight, obviously I don’t know that that’s going to happen and right now I cannot see how she gets this deal through the House of Commons.
“Now you know a week is a long time in politics as the old saying goes and in this climate a day, a few hours, is a long time in politics but right now things are looking extremely dicey for the Prime Minister and who knows whether she’ll still be in office by the end of the week, let alone by the 29th of March.”
Following the release of the 585-page agreement document, Jacob Rees-Mogg - the leader of the pro-Brexit European Research Group - wrote to all Tory MPs urging them to vote against it.
Rumours continued to swirl at Westminster that the tally of Conservative MPs who have submitted letters of no confidence in Mrs May is about to reach the 48 threshold needed to trigger a vote on her position.
"Certainly this has dented my confidence," he told ITV's Peston programme. "Politics depends on trust and this document is shattering to trust."
While the Cabinet agreed to collectively support the agreement, there was speculation that some ministers were so unhappy that they could still quit in protest.
Reports suggested as many as a third of the 28 ministers attending the meeting in No 10 voiced doubts about the deal.
Nick Timothy, Theresa May's former chief of staff, wrote in the Daily Telegraph that Parliament will "surely" reject the proposal.
"The proposal presented to Cabinet is a capitulation," he wrote.
"Worse, it is a capitulation not only to Brussels but to the fears of the British negotiators themselves, who have shown by their actions that they never believed Brexit could be a success.
"This includes, I say with the heaviest of hearts, the Prime Minister."
Work and Pensions Secretary Esther McVey was said to be particularly upset amid reports she was shouted down after she tried to press for the agreement to be put to a vote.
Mrs May described the debate around the Cabinet table as "long, detailed and impassioned", in a clear indication her proposals had come under intense challenge from ministers.
Speaking outside 10 Downing Street minutes after the meeting concluded, she acknowledged she faced "difficult days ahead" as she attempts to win round critical MPs.
"I firmly believe, with my head and my heart, that this is a decision which is in the best interests of the United Kingdom," she said.
At the same time she warned Brexiteers that if they failed to back her plan they risked ending up with "no Brexit at all".
Chief Whip Julian Smith has said he is confident the Government will get the support of Parliament for the deal.
But with the DUP - whose 10 MPs prop up Mrs May in the Commons - voicing their unhappiness at the agreement, and the prospect of a significant Tory backbench revolt it is hard to see how ministers can make the numbers add up.
Jeremy Corbyn again made clear that Labour was unlikely to come to the Government's rescue.
"I don't believe that the deal that I've heard of so far is in the national interest. It doesn't meet the interests of all parts of Britain, it doesn't give us a security of our trading relationship with Europe in the future," he said.
Meanwhile European Commission president Jean-Claude Juncker issued a statement that "decisive progress" had been made, clearing the way for a special summit for leaders of the remaining 27 EU states to give their stamp of approval, probably on November 25.
Senior UK Government officials said the final text of the withdrawal agreement featured important gains for the UK on the so-called backstop arrangements to be implemented if no trade deal can be reached.
The outline political declaration - which will be subject to further negotiation over the coming weeks - expresses an ambition to achieve zero tariffs and no quotas in EU-UK trade, something the officials said no other major economy had achieved.
The facilitated customs arrangements and "common rulebook" proposed in Mrs May's Chequers plan are replaced by the concept of a "sliding scale" of commitments and market access, which means the UK would not be tied to an off-the-shelf deal of the kind previously offered to countries such as Canada.
Under backstop arrangements designed to keep the Irish border open, if no trade deal is agreed by the end of the transition period in December 2020, a temporary "EU-UK single customs territory" would be established.
This could be terminated only by mutual consent of Brussels and London but each side would be legally bound to make "best endeavours" to bring it to an end by sealing a permanent deal on their future relations.
There will be a provision to allow the two sides to extend the transition to a fixed date rather than activate the backstop.
A five-person arbitration panel, with two representatives of each side and one independent member, will be set up to rule on disputes, with the chair chosen by drawing lots if members cannot agree.