The former foreign secretary said she had “gone into battle with the white flag fluttering over our leading tank”, with the EU.
The prime minister has previously insisted into the next general election, but a number of Tory MPs are said to be ready to back any moves to topple her leadership.
But what do they need to do to force a leadership challenge?
:: The magic numbers - 1922 and 48
Image: A leadership contest will be triggered if the 1922 committee receives 48 letters
Mrs May‘s fate hangs in the balance of the 1922 committee - the group of all backbencher Conservative MPs.
To trigger a vote of no confidence, its chair has to receive letters from 15% of them - 48 at present - formally calling on the leader to stand down.
The process is completely blind, though, so only the current chair Graham Brady knows how many letters have been submitted and by whom.
Several MPs publicly announced they had put in letters as part of a bid to unseat Mrs May in July, following the resignations of Boris Johnson and former Brexit secretary David Davis.
They remain on file, unless withdrawn.
When 48 letters are submitted, it triggers a confidence vote.
The prime minister needs a simple majority - half their MPs‘ votes plus one - to win. If they do, they get immunity from another formal challenge for a year.
:: What happens if they lose the confidence vote?
Image: Sir Graham Brady is the chairman of the 1922 Committee
A date for the first round of the leadership election would be chosen by Mr Brady, in consultation with the prime minister.
Contenders to replace them will be nominated, but must get the backing of 15% of Tory MPs.
Depending on how many candidates there are, rounds of elections will be held, with the MPs with the fewest votes dropping out of the race one by one.
That all changes when there are two candidates left - Conservative Party members will have the final say in an open election.
Mrs May managed to win without going through this final phase, because her opponent, now-Commons leader Andrea Leadsom, dropped out for suggesting .
If there is a contest, the winner will be announced by Mr Brady.
If all of Parliament wants to get rid of the prime minister, it has to table .
All 650 MPs would get the chance to vote formally on whether Mrs May should stay leader or resign, with the expectation a general election would follow.