Theresa May has written to all 317 Tory MPs, urging them to unite behind a Brexit deal while warning them history will judge us all over the process. Efforts will resume this Monday to persuade the EU to agree changes to the backstop plan to prevent the return of customs checks on the Irish border.
Culture Secretary Jeremy Wright has hinted MPs' concerns about it could be addressed without reopening the deal. Labour says the Tories cannot be united and has called for cross-party talks.
The UK remains on course to leave the EU on 29 March. But Mrs May has been unable to convince a majority of MPs to back the withdrawal terms she struck with the EU last year.
The prime minister told MPs in the letter she will return to Brussels to meet European Commission President Jean-Claude Juncker this week, and speak to the leaders of every EU member state over the coming days.
Her main goal is to win concessions over the backstop, which is widely disliked by members of her party. Many fear it will mean the UK staying closely aligned to EU rules for the long term, without Britain being able to end the agreement unilaterally.
But EU leaders have repeatedly said the withdrawal agreement s not open to negotiation. The Sunday Times reported comments it said were leaked from a WhatsApp group suggesting ex-Brexit minister Steve Baker told fellow Brexiteers that Mrs May's talks with Brussels were a complete waste of time.
However, Culture Secretary Mr Wright has hinted that there might be a number of different ways around the problem.
I don't think it's the mechanism that matters, it's the objective, he told the BBC's Andrew Marr Show, when asked whether a codicil - a supplementary document explaining or modifying a legal agreement - might work.
Parliament needs to give the prime minister space to have that conversation with Brussels, he added.
Attorney General Geoffrey Cox, who has warned the backstop indefinitely commits the UK to EU customs rules if Brexit trade talks break down, will set out what changes would be needed to address concerns in a speech on Tuesday.
Brexit Secretary Stephen Barclay is also due to meet the EU's chief negotiator Michel Barnier to discuss the controversial policy on Monday.
If MPs do not approve a formal deal, many fear chaos at ports and for business.