The PM bottled it yesterday as she pulled a key vote amid fears the government would suffer a humiliating defeat in the House of Commons.
European leaders will now be wooed by May in a bid to sweeten the divorce agreement – before putting it again to MPs for the final “meaningful vote”.
Doubts still loom if May will ever be able to get her deal through the Commons, and Tory rebels are now calling for their colleague to trigger a vote of no confidence.
Brexit supporter Steve Baker MP has urged his party to "change prime minister, and change prime minister now”.
And May will bring her Brexit deal back to the House of Commons "before January 21", the Prime Minister's official spokesman has said.
“You must be brave and make the right decision to change prime minister, and change prime minister now”
Steve Baker MP
Baker urged fellow Tory MPs to put in no-confidence letters to reach the 48-letter mark that would trigger a formal challenge.
Conservatives have to submit their letters to the partys ruling 1922 Committee.
Numerous letters have already been submitted following a failed coup by European Research Group (ERG) chief Jacob Rees-Mogg last month.
ERG deputy chairman Bakers scathing attack on May on the Today programme came as the PM also faces pressure from Labour, the SNP and the Liberal Democrats.
LAST DITCH: Theresa May meets with Mark Rutte as he tour of Europe begins (Pic: REUTERS)
Baker said: "Of course, we have all taken a bit of a bruising on this and it is a grave decision for every colleague to make.
"But what I would say to my colleagues is: you now face the certainty of failure with Theresa May, you must be brave and make the right decision to change prime minister, and change prime minister now."
Westminster chaos reigned yesterday as Mrs May's government pulled plans for the vote just hours after Downing Street had unequivocally confirmed the vote was going ahead.
The PM faces shouts of "resign" as she endured the bruising appearence in the House of Commons.
Ahead of his meeting with Mrs May later toyda European Commission President Jean-Claude Juncker has said the Brexit deal on offer has "no room whatsoever for renegotiation".
'MAY GONE TODAY': Steve Baker MP has called for MPs to oust the PM (Pic: FACEBOOK/STEVEBAKER) Related Articles
NO CONFIDENCE: Scottish First Minister Nicola Sturgeon is calling for a vote of no confidence (Pic: AFP)
Scottish First Minister Nicola Sturgeon accused Jeremy Corbyn and his Labour Party of stalling on supporting either a parliamentary confidence motion in Theresa May's leadership or a second referendum.
The SNP leader revealed her party had held talks with the official opposition in Westminster on Monday about the next steps to take.
She told Today: "As I understand it, they don't think the time is right for a motion of confidence.
"For goodness sake, if the time is not right now, when will the time be right?
"The clock is ticking, time is running out and if there is to be a different path found – and there must be a different path found to the one that Theresa May currently has the UK on – there isn't time to lose."
BRUSSELS: Jean-Claude Juncker has said there will be no renegotiation on Brexit (Pic: EPA)
Commons leader Andrea Leadsom suggested that Theresa May was seeking changes that would give Parliament an additional "democratic ability to decide".
She told Today: "That might include an addendum to the Withdrawal Agreement that sets out that Parliament will vote prior to going into a backstop, should that prove necessary, and potentially that the EU parliament and UK parliament must vote every year thereafter to provide that legitimacy for the UK to stay in the backstop, should that prove necessary.
"So there are plenty of options for the PM to talk to the EU about that don't involve reopening the Withdrawal Agreement, but that would provide the legal text as a part of the Withdrawal Agreement, through perhaps an addendum."
She also attacked Commons speaker John Bercow and appeared to question his impartiality over Brexit after the two clashed during yesterday's debate in Parliament.