With Britain's departure from the European Union on March 29, 2019 looming, there are growing concerns that a deal on the post-Brexit relationship may not be cobbled together in time to ensure a smooth and orderly British exit.
"We need to try and finalise a withdrawal treaty that is a legal document which is, to quote Michel Barnier, 87% completed but the remaining 12 or 13% involves Irish issues and the most hard is the Irish backstop commitment in terms of following through in that".
"The Irish border issue remains the chief stumbling block to a deal, while the European Union prepares for a November summit where it hopes an agreement will be sealed". But Britain rejects the EU's proposal, which would keep Northern Ireland inside the bloc's customs union while the rest of the United Kingdom leaves.
She also hit back at whispers in Brussels of a referendum on the final Brexit deal, saying: "We all recognise that time is short but delaying or extending these negotiations is not an option".
"If the European Union wants a proper trade deal with us, it is time they wised up to these facts and it is also time that they realised we are serious about walking away with no deal".
It feels that the search for something else has been in vain.
Despite the comments from Mr Muscat and Mr Babis, the Prime Minister showed no intention of giving ground on the issue of a so-called People's Vote when asked about it at the summit on Wednesday.
But to kick out publicly as they did in Salzburg certainly runs the risk of pushing Mrs May too far. Brexit supporters say such fears are exaggerated and Britain would thrive in the long term.
If May fell, selection of a new party leader would delay already tight Brexit negotiations.
"They build up, there's tough language and actually a deal is done at the last".
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Mr Varadkar added: "I'm not going to make compromises here [in the media]".
The decision of the British people was "pushed by those who predicted easy solutions", the French president said.
But he added negotiations were not yet at an "end game" and said Chequers was "broadly" a package that could get through Parliament.
Her former Brexit Minister David Davis has warned that there is, what he called, a rock solid core of 40 MPs who would vote against any plan reached under Mrs May's Chequers proposals.
He told HuffPost UK that, with Labour also planning to vote against Mrs May's plan, the "critical size of the voting bloc is quite small, it's basically a dozen people".
The Alpine summit began with a warning from EU Council President Donald Tusk that Britain's offer on post-Brexit trade ties and Ireland - the two sticking points in the talks - must be "reworked".
Britain's Prime Minister Theresa May addresses a press conference at the end of the EU Informal Summit of Heads of State or Government at the Mozarteum University in Salzburg, Austria, on September 20, 2018.
"Everybody shared the view that while there are positive elements in the Chequers proposal the suggested framework for economic cooperation will not work", he said.
The Prime Minister said the Chequers blueprint is the only proposal on the table as the deadline approaches, with the next leaders' meeting in October set to be a "moment of truth".
However, leader said afterwards there had been no progress on Brexit and.
"Those who explain that we can easily live without Europe, that everything is going to be all right, and that it's going to bring a lot of money home, are liars", Macron said of the British politicians who campaigned for withdrawal.
But Tusk said that was now contingent on May reworking her Chequers plan by Ocotber.