Theresa May is battling to save her Brexit strategy amid warnings that she is heading for another crushing defeat in Tuesday's crunch Commons vote.
Conservative Brexiteers said rejection of the Withdrawal Agreement was "inevitable" unless the Prime Minister was able to secure significant changes to the Northern Ireland backstop.
"Technical" talks between officials took place in Brussels over the weekend and Mrs May spoke to European Commission president Jean-Claude Juncker on Sunday night, although a Downing Street source said the negotiations were "deadlocked".
Some senior Conservatives said on Sunday that the prime minister should postpone the "meaningful vote" rather than risk another damaging reverse.
Instead she was being urged to table a "conditional" motion setting out the terms for dealing with the backstop issue which Parliament would be prepared to accept.
Conservative MP Andrew Bridgen said he would not be “surprised” if Theresa May postponed the vote on Tuesday.
He told talkRADIO’s Julia Hartley-Brewer: “It is a crucial week but they have all been crucial weeks. It would not surprise me if Theresa May did not call the vote in the end if nothing comes from the European Union.
“It would surprise me if the votes on no-deal and extending Article 50 were also not called.”
'A free vote'
Meanwhile, Public Health Minister Steve Brine has warned that he will resign unless Tory MPs are given a free vote in a vote expected later in the week on whether Britain should leave the EU without a deal.
"I think a free vote would be very smart," he told BBC Radio 4's The Westminster Hour.
"I would find it very difficult, actually impossible to be part of a policy that was pursuing actively no-deal."
The calls for a postponement came after former Cabinet minister Nicky Morgan warned that Mrs May's position would become untenable if Parliament "dismantled" her Brexit policy in a series of votes during the course of the week.
Nevertheless, delaying the meaningful vote would be another humiliation for the Prime Minister after senior ministers spent the weekend insisting it would go ahead as planned.
Mrs May had already postponed it once from December, only to see it resoundingly defeated the following month by a majority of 230.
With less than three weeks to Brexit Day on March 29 - when Britain is due to leave the EU - any delay would raise renewed questions as to whether there was any way she could get her deal through the Commons.
Mrs May has said if she loses the vote on Tuesday, there will be further votes on Wednesday on whether the UK should leave with no-deal and on Thursday on whether they should seek an extension to the Article 50 withdrawal process.