Theresa May is set to meet key EU figures for crunch talks which could determine whether she is able to secure a Brexit deal.
The Prime Minister will meet European Commission president Jean-Claude Juncker and Donald Tusk, the president of the European Council, on Monday amid warnings from Tory Brexiteers not to give any more ground to Brussels.
The meeting in the Belgian capital marks the deadline set by Mr Tusk for Mrs May to come forward with an improved offer on the terms of Britain's withdrawal.
Without it, Mr Tusk has said he will be unable to recommend EU leaders give the green light for the second phase of negotiations - to include talks on a free trade agreement - to begin at their summit on December 14 and 15.
Downing Street sought to play down the significance of the encounter, describing it as a "staging post" on the route to the full gathering with the other 27 leaders in the middle of the month.
"With plenty of discussions still to go, Monday will be an important staging post on the road to the crucial December council," a Government spokesman said.
However her room for manoeuvre appears to be limited, with hardline Brexiteers urging her to walk away from the negotiating table altogether if EU leaders refuse to sanction the start of the phase two talks.
Health Secretary Jeremy Hunt urged Tory MPs to rally behind the Prime Minister, suggesting that without her there would be "no Brexit".
"The choice we face now is not between this Brexit and that Brexit, if we don't back Theresa May we will have no Brexit and she is doing an unbelievably challenging job amazingly well," he told ITV's Peston On Sunday.
While two sides appear to be moving closer on the UK's divorce bill and future citizens' rights, it is unclear whether they can bridge the gap on the Irish border - the third area where Brussels is demanding progress.
Mr Tusk has made clear that the phase two talks cannot begin unless the UK can satisfy Dublin that there will be no return to a "hard border" between Northern Ireland and the Republic.
Ireland's deputy prime minister Simon Coveney insisted that they were not seeking to delay the process. "We certainly don't want to be vetoing anything," he told BBC One's The Andrew Marr Show.
However the influential German MEP David McAllister, who is close to Chancellor Angela Merkel, said it was proving "very, very complicated".
"Experts have been working on this issue now for months, and they still haven't come up with a solution. I would say at the moment it's still a 50-50 situation," he told Peston On Sunday.
Meanwhile a series of prominent Conservatives including Jacob Rees-Mogg, John Redwood and former chancellor Lord Lawson signed a letter calling on her to refuse to settle the UK's "divorce bill" unless Brussels agrees to a series of new demands.
They include settling the terms of a free trade agreement "in principle" by the end of March 2018 and an end to the jurisdiction of the European Court of Justice and the freedom of movement to the UK for EU nationals when the UK leaves a year later on March 30 2019.
Other signatories to the letter, organised by the Leave Means Leave group, include Conservative former ministers Owen Paterson and David Jones and the Labour MP Graham Stringer.