Britain is now not set to leave the EU until October 31 – and the fight is now on for European Parliament election.
The PM will then resume cross-party talks with Labour in a bid to finally make some progress of Britains exit from the EU.
And the days proceedings have already begun under a cloud for May, as Tory MP Nigel Evans has called for her to resign “today”.
The joint executive secretary of the Tories ruling 1922 Committee told the BBC Today programme the Conservatives need new leadership and that the process "can't start soon enough".
“I believe the only way we're going to break this impasse properly is if we have fresh leadership”
Nigel Evans MP
Mr Evans said: "To be honest I would be delighted if she announced today she was announcing her resignation and we could then have an orderly election to choose a new leader of the Conservative Party.
"I believe the only way we're going to break this impasse properly is if we have fresh leadership of the Conservative Party…
"If there was an announcement today by the Prime Minister then of course we could start the process straight away."
May had previously suggested she may quit – but has remained as PM as she continues to rally support for her deal.
GONE BY TOMORROW?: Theresa May has been urged to quit as Prime Minister (Pic: PA)
It emerged the PM could face an unprecedented vote of confidence in her leadership after 70 local Conservative association chiefs signed a petition in support of a poll.
They called for an extraordinary general meeting of the National Conservative Convention to discuss the Prime Minister's leadership of the party, the Telegraph reported.
A non-binding vote is expected to be held at the meeting, which would – if it showed a lack of confidence – put pressure on the 1922 Committee of Tory MPs to find a way of forcibly removing the PM from office.
May has come under heavy criticism for her handling of the Brexit process, but survived a vote of confidence by her MPs in December after a coup spearheaded by Jacob Rees-Mogg.
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Under party rules a year has to pass before another vote can be called, but an extraordinary general meeting must be held if more than 65 local associations demand one through a petition, the paper said.
Elsewhere a new poll found former foreign secretary and longterm May rival Boris Johnson is the favourite to replace her as Conservative leader among the party's grassroots.
Almost a third of party members – 32.4% – backed the pro-Brexit Tory to take over the helm of the party, up by 10 points in the last month.
Ex-Brexit secretary Dominic Raab was second with 14.7%, according to the poll of 1,128 panel members by the Conservative Home website.
Environment Secretary Michael Gove, who also supported the Leave campaign, came third, ahead of Foreign Secretary Jeremy Hunt and Home Secretary Sajid Javid.
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