Theresa May has been urged to delay the "meaningful vote" on her Brexit deal for a second time.
Former Brexit secretary David Davis has speculated the vote could be put off if Mrs May looks likely to lose it.
His comments come as the Prime Minister prepares to meet EU leaders and seek further "clarifications" in a bid to persuade sceptical MPs to back her deal.
She is expected to speak this week to EU leaders including German chancellor Angela Merkel, Dutch prime minister Mark Rutte and European Council president Donald Tusk in an attempt to break the Brexitlogjam, the Financial Times has reported.
A Downing Street source told the Press Association that talks between Mrs May's negotiators and their counterparts in Brussels have continued over the Christmas period.
Mr Davis, in a column for the Daily Telegraph, insisted a deal will be reached "at the eleventh hour" because the EU is worried about losing the £39 billion "divorce payment" that would come with a Brexit deal.
The vote, which was delayed at the last minute in December, is currently scheduled for the week beginning January 14.
Mr Davis said: "The Withdrawal Agreement does not respect the referendum result. That is why the meaningful vote had to be delayed and one wonders if even the January vote will go ahead.
"Attempts to frighten MPs into supporting it are unlikely to work, because voting down this substandard deal will not result in no Brexit."
Urging Mrs May to take her time to get a better deal, he adds: "We know that the EU is worried about the loss of the £39 billion 'divorce' payment if there is no deal... so this is the moment to be hard-nosed about these issues.
"The more we prepare to leave the EU without a deal, the more likely a good deal becomes.
"Tory MPs must remain committed to delivering the referendum result, as repeated in our manifesto, which pledged to leave the Customs Union and the Single Market and which said that no deal is better than a bad deal. To do otherwise would frankly throw our democracy's credibility into chaos."
Meanwhile the current Brexit Secretary Steve Barclay is reported to be convening a meeting on Thursday of ministers to discuss the latest preparations for a no-deal Brexit.
Foreign Secretary Jeremy Hunt, speaking in Singapore, said cancelling Brexit through a second EU referendum would have "devastating" social consequences, while a no-deal exit would cause economic disruption.
He predicted the Government would "find a way" of getting the 585-page withdrawal agreement approved by Parliament.