In her defiant statement on the steps of Downing Street soon after the no-confidence vote was announced on Wednesday morning, May said changing the Conservative Party leader would "put our country's future at risk and create uncertainty when we can least afford it".
"She did say she wouldn't be fighting the next general election", Work and Pensions Secretary Amber Rudd told reporters.
"I think then what will and should happen is the Europeans will go off and have elections [.] and we will then have a proper Conservative leadership election, for a post-Brexit withdrawal, new generation Conservative who can reunite this party, this country".
Finnish prime minister Juha Sipilä told reporters: "Legally binding will be a little bit hard but anyway I think that we all want to help".
They have been largely unhappy with the Irish backstop proposal.
Oxford East Labour MP Anneliese Dodds said: "This is putting the interests of quite a small number of people first, who have quite extreme views, and putting them before the interests of British business, our universities and all the European Union citizens who are based here".
Many Conservative MPs are unhappy with the Brexit plan she negotiated in Brussels, and discontent reached a tipping point when she delayed a parliamentary vote on the deal which was scheduled for Tuesday.
By the time of the vote, Mrs May's survival looked assured, with the tally of Tory MPs publicly declaring they would support her passing the threshold of 159 needed to secure her position. The deal is likely to be voted on before January 21 and the delay may help the Government by convincing MPs they have no alternative.
But on Monday she pulled a parliamentary vote on her deal - which seeks to keep Britain closely aligned with the European Union after exit - to avoid defeat. With May ostensibly safe as leader for one year, will some of the 117, and indeed some of the ERG group, begin to break off the closer the meaningful vote in January gets?More news: Strasbourg Christmas market gunman 'shot dead'
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If May is toppled, the ERG will prove a potent force in selecting the party's next leader.
Thimont Jack said: "The confidence vote illustrates what we already knew to be the case, but at the same time, because you can't trigger another confidence vote for 12 months, so it does give May some breathing room".
He made the comments after a meeting with Prime Minister Theresa May.
Theresa May on Wednesday won by a large margin a confidence vote by her fellow Conservative members of parliament.
"The crisis and chaos now facing the United Kingdom is entirely a result of the vicious civil war that has engulfed the self-centred Conservative Party - at a crucial time in the UK's history, it has a lame duck Prime Minister saddled with a lame duck Brexit deal".
May responded to a no-confidence vote with a passion she reserves for when her back is against the wall, defending her Brexit deal and warning that ousting her could derail the whole process.
The EU's free trade agreement with Canada, for example, was held up by a vote in a regional Belgian parliament.
Jeremy Corbyn is allegedly plotting a no-confidence motion in parliament on Theresa May's government before Christmas, as reports emerge of talks taking place between the DUP and Labour to find "common ground".
The EU's top court ruled on Monday that Britain could cancel its Article 50 notice to leave without permission from other members and without losing privileges. Foster, whose 10 MPs prop up the minority Tory administration, said she told the May "we were not seeking assurances or promises, we wanted fundamental legal text changes".
At the very least it provides some certainty in that markets know the United Kingdom leader will remain unchanged during the crucial 2019 Brexit as a new leader might have been more inclined to opt for a "no deal" Brexit.