After a dinner of Wiener schnitzel in Salzburg, EU leaders said they will push for a Brexit deal next month but warned May that if she will not give ground on trade and the Irish border by November they are ready to cope with Britain crashing out.
The prime minister's personal plea for the 27 heads of government to back her Chequers proposals was greeted with a resounding "no" at a summit in Salzburg, Austria.
The Prime Minister went on to condemn European Council President Donald Tusk, who flatly rejected the UK's proposals at the Salzburg summit.
German Chancellor Angela Merkel said "substantial progress" was still needed and Dutch Prime Minister Mark Rutte said his country is better prepared for a no-deal Brexit than Britain.
May has said the Chequers proposals for trade with the European Union, which would resolve arguments over the border of Northern Ireland with the Irish Republic, were the only way forward.
May also spoke about the Irish backstop and the concept of "breaking up our country", saying: "We both agree that the Withdrawal Agreement needs to include a backstop to ensure that if there's a delay in implementing our new relationship, there still won't be a hard border between Ireland and Northern Ireland".
'So don't worry. Be happy, don't worry.' Mrs May was buoyed ahead of the talks when the EU's chief Brexit negotiator Michel Barnier said he hoped a deal could be sealed in six to eight weeks.
May's "Chequers plan" - named for the prime minister's country retreat where it was hammered out in July - aims to keep the U.K.in the European Union single market for goods, but not services, in order to ensure free trade with the bloc and an open border between the U.K.'s Northern Ireland and European Union member Ireland. The EU didn't call for a referendum, David Cameron's administration did - so the idea that the EU is "effectively dividing our country in two", as May put it, is flawed.
"Neither side should demand the unacceptable of the other, we can not accept anything that threatens the integrity of our union as they can not accept anything that threatens the integrity of theirs".
Mrs May said: "We can not accept anything that threatens the integrity of our union, just as they can not accept anything that threatens the integrity of theirs".
In a defiant final message, the prime minister said: "The EU should be clear: I will not overturn the result of the referendum".
UK Brexit Secretary Dominic Raab said the bloc had "yanked up the handbrake" on the negotiations.
Despite all the heated British rhetoric, the EU's position is not new.
'We need serious engagement on resolving the two big problems in the negotiations.
'The backstop can not divide the United Kingdom into two customs territories, ' she said.
Dealing with the European Union is only part of May's problem.
By that time the leaders had already been through a scratchy four-hour debate on the migration crisis - a bigger concern than Brexit for many of them. To deny its legitimacy or frustrate its result threatens public trust in our democracy.