Mrs May’s aides are said to be at loggerheads this weekend over whether to accept a soft Brexit or call a general election.
Her team want to put her Brexit deal back to the Commons for a fourth vote early this week and if it fails again, some of her most senior aides are pushing for her to call a snap poll.
Brexiteer cabinet ministers are reportedly poised to resign if Mrs May accepted a soft Brexit involving a customs union or a long delay to the EU exit which involves taking part in the European elections.
One-hundred-and-seventy MPs and ministers have signed a letter urging the PM to secure a swift departure from the EU and pursue a no-deal exit rather than accept a soft Brexit. But at least six cabinet ministers in the Remain camp are prepared to quit if she allows the UK to crash out of the EU without a deal, according to the Sunday Times.
After MPs rejected Mrs May’s deal again on Friday by 58 votes, the PM said there would be "grave" implications and, in a hint at a general election, warned they were "reaching the limits of this process in this House".
Her comments set alarm bells ringing among MPs who fear the party is in no state to fight an election.
Mrs May would effectively be a lame duck leader - having said she will stand down once she has got Brexit through - and voters would be voting "blind" not knowing who her successor would be.
Foreign Office minister Sir Alan Duncan told The Observer: "If we have a general election before Brexit is resolved, it will only make things worse."
Under the terms of the Fixed Term Parliaments Act, the Prime Minister needs a two-thirds majority in order to call an election.
However, after her disastrous decision to go to the polls early in 2017, Tory MPs made clear they would not be prepared to support her in doing so again.
Pro-EU backbencher Antoinette Sandbach, who backs a second referendum, told The Observer: "The answer is not a general election, and I would vote against that. We need to find a way forward in Parliament."
Her comments were echoed by Mark Francois, the deputy chairman of the pro-Brexit European Research Group, who told the paper there was "not a chance" MPs would back an election under her leadership.
"Of course they wouldn't - not after last time. And remember, she needs a super majority to do it," he said.
Nigel Evans, executive secretary of the backbench Conservative 1922 Committee, said the Cabinet would block it.
"I don't believe the Cabinet would allow her to do it," he told the paper.
"Theresa May cannot call an election, she cannot be the leader who would lead us into it. The party would not tolerate it."
The warnings came as MPs prepared to take control again of the Commons timetable with a second series of "indicative" votes starting on Monday in attempt to find a alternative plan which can command a majority in the House.
Many Brexiteers fear the cross-party initiative - led by former minister Sir Oliver Letwin - will inevitably lead to a "softer" Brexit and a lengthy delay, or even no Brexit at all.
With frustrations growing on all sides at the continuing deadlock, it emerged that 170 Tory MPs had written to the Prime Minister demanding a swift departure - with or without a deal.
The letter was said to have been signed by 10 members of the Cabinet - including Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid - and 20 other ministers.
Conservative Party chairman Brandon Lewis confirmed the existence of the letter, saying: "I haven't signed the letter. I do know about it."
The letter followed a warning by the Prime Minister that an extended delay to Brexit was "almost certain" if her deal does not go through.
Following the defeat on Friday, she warned the Commons would not allow Britain to leave without a deal on April 12 - the new deadline set by the EU.
Any extension beyond that date would require Britain to take part in elections in May to the European Parliament - something Brexiteers are desperate to avoid.