10:10, 17.Dec 2018
Theresa May will urge the EU to help get her Brexit deal through the Commons by agreeing legally binding changes to the controversial backstop.
The EU has told the UK to come forward with new ideas to break the deadlock ahead of Tuesday's vote by MPs.
But Mrs May will say the EU has a "big choice" of its own to make, if it wants to ensure the UK leaves with a deal.
Jeremy Corbyn said Labour would not back the PM on Brexit until she dropped her opposition to a customs union.
The UK is due to leave on 29 March although Parliament has yet to agree the terms of withdrawal. MPs will hold a second "meaningful vote" on Tuesday on the agreement negotiated by Mrs May.
The BBC's political editor Laura Kuenssberg said only one minister had told her they believed Parliament would back the deal as it stood.
On a visit to a factory in Grimsby, Lincolnshire, later, Mrs May will say that "just as MPs will face a big choice next week, the EU has to make a choice too".
"We are both participants in this process. It is in the European interest for the UK to leave with a deal.
"We are working with them but the decisions that the European Union makes over the next few days will have a big impact on the outcome of the vote."
What is the sticking point?
The first vote, in January, saw the deal rejected by 432 votes to 202, the largest defeat for a sitting government in history.
Mrs May is seeking legally-enforceable changes to the backstop - a controversial insurance policy designed to prevent physical checks on the border between Northern Ireland and the Republic of Ireland - but there have been few visible signs of progress.
Leading Brexiteers are looking for reassurances that the backstop - which would see the UK aligned with EU customs rules until the two sides' future relationship is agreed or alternative arrangements worked out - will not endure indefinitely.
The European Commission said on Wednesday "no solution has been identified" to the Irish backstop and it has refused to rewrite the withdrawal deal already struck, which is designed pave the way for trade talks.
Foreign Secretary Jeremy Hunt told BBC Radio 4's Today that the UK's demands were "not unreasonable" and it was "entirely possible" there would be a breakthrough in the next 72 hours.
But Conservative MP Bill Cash, one of eight leading Brexiteers who will scrutinise any new legal text agreed by the two sides, said he could not see any way he could vote for the deal right now.
"The Withdrawal Agreement itself is so completely flawed that I couldn't possibly vote for it, simply on the grounds that it makes us a subjugated vassal state," he said.
And Labour Leader Mr Corbyn, who on Wednesday met Conservative MPs to discuss their alternative plan for a closer economic relationship with the EU, said the PM must relax her red lines on customs arrangements and market access.
"It is time the prime minister got on board and recognised that there is a deal that could command a majority in the House of Commons," he said on Friday.
He said the prime minister's calls for the EU to help break the deadlock "sound like an act of desperation".
Will Brexit be delayed?
If MPs reject the deal again, they will get to choose between leaving without a deal or deferring the UK's exit from the EU beyond the scheduled date.
Any extension to the Article 50 process, under which the UK is due to leave the EU on 29 March, would need the unanimous approval of the EU.
Two former prime ministers, Sir John Major and Gordon Brown, have called for a delay of a year to allow for a "public consultation" on the way ahead and to ensure an orderly exit.
Mr Brown told the BBC if Parliament could not resolve the situation "the only way that we can get unity in this country is by involving the people in trying to find the solution".
But Cabinet Brexiteer Liam Fox told the BBC's Newsnight programme he was concerned that Remain MPs may seek to wrest control of Brexit from the government next week.
"In Parliament there are a large number of MPs who do not see it as their primary objective to deliver the referendum and would want to keep us locked to the EU."
Does anyone really know what happens next?
Next week the prime minister is going to have another go at getting her deal through Parliament, which would reverse a record defeat of over 200 votes.
She's going to try with, she hopes, a new piece of legal and verbal gymnastics from her attorney general that is proving extremely difficult to nail down.
Number 10 is trying too, with a series of promises on issues like workers' rights to Labour MPs, and a cash fund that will be up for grabs for constituencies around the country, that have lost out to greedy urban giants.
But the mood is not good around the government.
Only one minister this week has told me they believe the deal will get through.