EU leaders have rebuffed May's request to sweeten the divorce agreement and help her win over a hostile UK Parliament, and Juncker complained to reporters about a political climate which was sometimes "nebulous, imprecise."
British Prime Minister Theresa May left the EU summit on Friday exactly as she had arrived – promising talks to extract reassuring words from EU leaders to help her sell the Brexit deal back home.
In the intervening hours those leaders had expressed frustration with May's "nebulous" strategy to get the withdrawal treaty past the House of Commons and insisted yet again that they will not renegotiate the text.
May nevertheless put a brave face on the apparent rebuff and set off back to London to restart plans to put the Brexit deal before parliament, just five days after she abandoned a scheduled vote in the face of mass opposition from her own MPs.
"There is work still to do and we will be holding talks in the coming days about how to obtain the further assurances that the UK parliament needs in order to be able to approve the deal," she said.
It was not immediately clear which further talks she was referring to, as the EU leaders had cut a clause from a draft declaration that would have promised "further assurances" on the border issue.
"I have no mandate to organise any further negotiations," said Donald Tusk, the summit host and president of the European Council, which represents EU leaders.
"We have to exclude any kind of reopening of negotiations on the withdrawal agreement but we will stay here in Brussels and I am always at Prime Minister May's disposal," he said.
TRT World's Simon McGregor-Wood has more.
'Clarify and reassure'
European officials said no further EU summits are scheduled before January 21 – by which time May has said the deal will have gone to parliament – and the British leader has not requested one.
"There is an agreement, the only and best deal possible and we cannot renegotiate it. But we can clarify and reassure," French President Emmanuel Macron said.
Instead, the Europeans called for more details from May as to how she intends to pass a withdrawal bill that, as it stands, is opposed by a clear majority of British lawmakers.
"The signals we heard yesterday were not particularly reassuring on Britain's capacity to honour the commitments that were made," Belgian Prime Minister Charles Michel said.
"So we will make sure to prepare for all scenarios and prepare also for a no-deal scenario."
On Thursday, European Commission President Jean-Claude Juncker complained that the strategy to steer a deal agreed on November 25 into law was "nebulous and imprecise."
Footage of the opening of Friday's talks showed May in a tense head-to-head with Juncker and lip readers told media she said: "What did you call me? You called me nebulous. Yes you did."
Irish Prime Minister Leo Varadkar told reporters that many EU leaders were concerned May was asking for concessions without being able to guarantee they would be enough to deliver the vote.
"That was a question that was asked by a lot of prime ministers: 'Is what you're asking for going to be enough?' Because if it's not enough there's no point giving it," he said.
But several other leaders defended May.
"She was very clear, very open about what she wants from us and we put it on paper," Dutch Prime Minister Mark Rutte said.
Britain's self-imposed deadline of January 21 to approve the deal is uncomfortably close to Brexit day on March 29, 2019 – and Europe is stepping up preparations for a no deal.
'She left with less'
May had come to Brussels wounded by a confidence vote on Wednesday night, which she won but in which more than one-third of her Conservative party MPs voted to oust her.
Opposition to the deal in Britain is focused on a so-called "backstop" arrangement designed to keep the border with Ireland open unless and until a new UK-EU trade deal is signed.
May is seeking "legal and political assurances" that this will not keep Britain trapped indefinitely in an EU customs union.
But, while an early draft of the conclusions said the EU "stands ready to examine whether any further assurances can be provided", this was removed from the final version.
"Colleagues were so exasperated that she left with less than she could have got," a European source said.
May nevertheless welcomed the short joint statement.
"As formal conclusions, these commitments have legal status and therefore should be welcomed," she told reporters, but added: "MPs will require further assurances."
Arlene Foster, leader of Northern Ireland's hardline DUP made it clear that it would no longer prop up May's wafer-thin Commons majority if she pushes on the with the plan.
"This is a difficulty of the Prime Minister's own making. A deal was signed off which the Prime Minister should have known would not gain the support of Parliament," she said.