In Britain, Cabinet Office Minister David Lidington, a senior May ally, insisted Thursday's talks in Brussels had been "a welcome first step", noting that the European Union had said it wanted a "speedy United Kingdom trade deal" after Brexit.
But her allies claimed her 200 votes she won were one more than the 199 when she secured the Tory leadership in 2016 and were relieved that she can not be challenged again for another 12 months.
Liam Fox, the worldwide trade minister, said Thursday the Cabinet could block May from bringing her exit withdrawal deal before the House of Commons next month and that it might insist Britain's scheduled departure date of March 29 be moved back several months to provide time for a fresh approach.
"I don't expect an immediate breakthrough, but what I do hope is that we can start work as quickly as possible on the assurances that are necessary", Mrs May said.
An EU diplomat told CNN before the meeting that the other 27 EU nations were looking to May to "convince" them she can get the withdrawal agreement through the UK Parliament, something she appears to have failed to do.
Leaders are likely to be called back to Brussels a second special Brexit summit in January to sign-off written assurances of some sort, according to two European Union diplomats spoken to by Yahoo Finance UK.
After a whistlestop tour of European capitals on Tuesday, she said on Wednesday she would continue to seek "legal and political assurances" over the temporary nature of the so-called "backstop".
The Brexit withdrawal agreement only talks about "best endeavours" being used to reach an agreement during the transition period.
"There is nobody in his right mind in the European Union who wants to trigger the backstop because it is bad news not only for the United Kingdom but for the EU". Leaders all ruled out new, legally binding accords to amend the package. "We can add some clarifications but there will be no renegotiations".
She then went on to win a confidence vote brought by her own MPs but vowed to listen to the concerns of the 37% of Tory MPs who voted against her.
Mrs May spoke of a "renewed mission - delivering the Brexit people voted for, bringing the country back together and building a country that really works for everyone".
Instead, the Europeans called for more details from the prime minister as to how she intends to pass a withdrawal bill that, as it stands, is opposed by a clear majority of British lawmakers.
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Mueller is also probing whether any foreign cash flowed to the inaugural fund, which is prohibited from accepting foreign funds.
Austrian Chancellor Sebastian Kurz added on Friday: "There is a withdrawal deal, and there is an urgent necessity to take decisions".
"We have treated prime minister May with the greatest respect, all of us, and we really appreciate the efforts by the prime minister to ratify our common agreement", Tusk said.
How have Conservative MPs reacted?"But of course we will stay here in Brussels, and I am always at prime minister Theresa May's disposal".
If Google users are any guide, a lot of people are still getting to grips with the issue that has dominated United Kingdom politics for the past three years.
Earlier the tensions erupted into public view when a visibly angry Mrs May was seen berating European Commission president Jean-Claude Juncker over remarks he had made during the press conference in the early hours of Friday.
He also criticised the UK's lack of clarity over the future relationship it is seeking with the European Union once it has left.
What are the opposition saying?
May said she would fight for her job with everything she had.
May has also faced constant criticism of her Brexit strategy from hard line anti-Europeans in her party.
"The problem is the MPs in London", he said.
He said a lot of leaders were called to such a summit at the end of November and he did not believe they would be willing to come again at short notice.
"I don't think this vote really changes anything very much in terms of the arithmetic", he told BBC News.