The cabinet will discuss whether the government should ramp up preparations for a no-deal Brexit when it meets later this morning.
It comes after Theresa May said MPs would not vote on her Brexit deal until the third week in January.
A Labour motion of no confidence in Mrs May was dismissed by No 10 as “silly political games” on Monday evening.
Labour leader Jeremy Corbyn is under pressure to push for a further vote of no confidence – in the government.
With 101 days left until Brexit and many MPs still opposed to the government’s withdrawal agreement, ministers are due to consider a paper on plans for leaving the EU without a deal.
But a no-deal Brexit is also opposed by many MPs.
A cross-party group of 60 of them have written to the prime minister, saying it would do “unnecessary economic damage”.
Mr Corbyn tabled a motion on Monday night, calling on MPs to declare they have no confidence in the prime minister because she failed to have a vote on her Brexit deal straight away.
No 10 refused to make time for the motion.
Other parties – the SNP, Lib Dems, Plaid Cymru and Greens have called on Mr Corbyn to push for a no-confidence vote against the government as a whole.
Unlike a vote aimed at the prime minister, the government would have to allow a vote on this motion and, if successful, it could force a general election.
However, Nigel Dodds, deputy leader of Northern Ireland’s DUP, which has propped up the Conservative government since June 2017, dismissed Mr Corbyn’s move as “parliamentary antics”.
Mrs May also appeared to have the support of pro-Brexit backbench critics who last week failed in a bid to oust her as Tory leader.
One of them, Steve Baker, said: “Eurosceptic Conservatives are clear that we accept the democratic decision of our party to have confidence in Theresa May as PM. We will vote against Labour in any confidence motion.”
On Tuesday, the Daily Telegraph published a letter by 52 business leaders, including former Sainsbury’s boss Justin King and Glastonbury Festival founder Michael Eavis, calling on the prime minister to “take her deal to the British people”.
“The prime minister abandoned the most important vote in the House of Commons for a generation because she knew she could not secure a parliamentary majority for her deal,” they wrote.
They said last week’s rebellion by her own MPs “underlines the impossibility of resuscitating it”.
The prime minister’s Brexit deal sets out the terms of Britain’s exit from the EU – on 29 March 2019 – and includes a declaration on the outline of the future relations between the UK and the EU.
But the deal only comes into force if both parliaments approve it.
The PM had delayed the vote from last week, admitting she looked set to lose.
Mrs May told MPs they would have the chance to vote on the deal she negotiated with Brussels in the third week of January.
She said she had won fresh guarantees at last week’s EU summit over measures to avoid a hard border on the island of Ireland and she hoped to secure additional “political and legal assurances” in the coming weeks.
Earlier on Monday, an EU spokesman said it had provided the “clarifications” requested on the contentious issue of the Northern Ireland border backstop and “no further meetings were foreseen”.
Mr Corbyn said by January a month would have been wasted since the original 11 December vote was postponed, with “not a single word renegotiated and not a single reassurance given”.
“The deal is unchanged and is not going to change,” he said.
By Laura Kuenssberg, BBC political editor
Keeping up? I don’t blame if you if it all seems like procedural nonsense. And frankly, you might not be completely wrong.
But what it suggests is that despite widespread frustration on all sides, Jeremy Corbyn is so far stopping short of taking a real shot at toppling May’s administration, and is unlikely to do so unless, and until, he thinks he can win.
For her part, Theresa May is unlikely to budge on her plan, unless and until she is forced to do so.
To the immense irritation of both their supporters and their rivals, even though the Brexit clock is running down, neither of the main party leaders are willing to take the kind of radical move that might unblock the gridlock.