Theresa May will try to rally ministers behind her this morning at the start of a critical 48 hours for Brexit.
On Monday, the PM told MPs an agreement with the EU was "still achievable" despite apparent deadlock over the issue of the Irish border.
EU officials, though, have warned no-deal is "more likely than ever before".
The clock is ticking down towards a summit of European leaders on Wednesday where it had been hoped a deal could be reached.
The latest Brexit developments:
A group of Brexit-supporting ministers met in the Commons on Monday night - apparently over pizza - to discuss the way forward, but the BBC has been told that no resignations are imminent.
The Democratic Unionist Party - whose backing Theresa May needs to win key Commons votes - is warning that it is prepared to "paralyse" her domestic agenda if she undermines Northern Ireland's position within the UK in the Brexit negotiations.
The Austrian foreign minister, along with several senior EU officials, have told the BBC they feel the chances of Wednesday's summit being "the moment of truth" for Brexit have diminished significantly.
German Chancellor Angela Merkel said Berlin wants the UK's withdrawal next March to be orderly "but not at any price", while Irish premiere Leo Varadkar suggested a deal may be delayed as late as December.
The UK is due to leave the EU in March and it had been hoped that on Wednesday EU leaders would agree that enough progress had been made to call a special summit in November to finalise the divorce deal and set out a political statement on post-Brexit trading relations.
However, hopes of that happening were dealt a major blow on Sunday when ministers failed to make anticipated progress on the Irish border problem.
Nevertheless, the prime minister said on Monday that the two sides were not "far apart" and the border issue must not be allowed to derail the entire effort.
She tried to reassure MPs the UK would not end up in "permanent limbo", tied to the EU's customs rules, and did her best to convince the DUP's leaders that she would not sign up to any deal which created a new border between Northern Ireland and the rest of the UK.
Labour leader Jeremy Corbyn dismissed her comments as "another 'nothing has changed' moment from this shambles of a government".
The prime minister will continue efforts to win senior ministers over at a cabinet meeting on Tuesday morning.
Former Brexit minister Steve Baker told BBC Two's Newsnight the cabinet needs to "change the prime minister's mind" on her plans or they will be rejected.
Mrs May has repeatedly warned that failure to reach agreement over the border could result in the UK leaving the EU without a deal in March next year.
Much of the focus is now on the so-called backstop.
Both the UK and the EU both want to avoid a "hard border" - physical checks or infrastructure between Northern Ireland and Ireland after Brexit.
Agreeing how that can be done has so far proved impossible and the backstop is the position of last resort - a safety net that will apply if a wider deal or technological solution cannot keep it as frictionless as it is today.
The EU has proposed a backstop that would mean Northern Ireland staying in the customs union, large parts of the single market and the EU VAT system - the UK has rejected this because of fears it would create what would be effectively a border between Northern Ireland the rest of the UK.
The UK is instead proposing a backstop which would effectively keep the whole of the UK in the EU customs union for a limited period.