Prime Minister Theresa May is expected to update ministers on her Brexit strategy when she chairs a meeting of her cabinet this morning.
It comes after a weekend of speculation about her leadership and claims of a plot to oust her – something senior ministers have denied.
There have been suggestions that naming a date for her departure as PM could boost support for her Brexit deal.
But Downing Street has refused to be drawn on Mrs May’s future.
The Sun newspaper has used its front page to urge Mrs May to set a date for her resignation to win over reluctant Tories and the Democratic Unionist Party in order to bolster the chances of her withdrawal agreement passing in a third vote.
Her deal has been overwhelmingly rejected in the Commons twice, and it remains unclear whether she will bring it back a third time this week after she wrote to MPs saying she would only do so if there was “sufficient support”.
Conservative MP Nigel Evans told BBC Radio 4’s Today programme that that Mrs May should get her deal over the line first, and then resign so that there can be an “orderly replacement” of the prime minister, with no need for an interim caretaker.
Mr Evans, a joint executive secretary of the 1922 Committee, added: “Clearly a number of people do not want the prime minister anywhere near the next phase of negotiations, which is the future trading negotiation between ourselves and the EU.”
The cabinet meeting later follows intense speculation over the weekend about Mrs May’s premiership following a week in which she was forced to ask the EU for an extension to Article 50, and criticised for blaming the delay to Brexit on MPs.
On Sunday, amid reports of a plot to replace Mrs May with a caretaker prime minister, two cabinet ministers touted as potential successors said they fully backed the PM.
As senior figures dismissed talk of a “coup”, Mrs May summoned leading opponents of her deal to Chequers, her country retreat, to assess whether there is enough support for it to bring it back to the Commons this week.
But after lengthy talks with prominent Brexiteers – including Boris Johnson, Jacob Rees-Mogg and Iain Duncan Smith – there was little sign of an immediate breakthrough.
This afternoon MPs are expected to back a plan to carve out parliamentary time for a series of so-called indicative votes on alternatives to Mrs May’s deal, prompting concern in No 10.
As many as six other options, in addition to Mrs May’s deal, could be put to votes to see which are most popular.
Conservative MP Sir Oliver Letwin, who is spearheading the move, told the Today programme that once Mrs May knows what it would take to get a majority vote, it would help her find “a way forward in principle”.
Brexit Secretary Steve Barclay warned on Sunday that the risk of a general election would increase if MPs took control of parliamentary proceedings and brought about a “constitutional collision”.
But Chancellor Philip Hammond said “one way or another” MPs would be given the opportunity this week to decide what it is in favour of, though he would not confirm whether Tories would be given a free vote on the options.
Boris Johnson has described some of the suggested options – including a Norway-style close relationship with the EU – as “catastrophic” in an article in the Daily Telegraph.
Accusing Mrs May of “bottling” Brexit, the former foreign secretary said the only argument for backing what he called her “rotten deal” was if every other option was worse.
Meanwhile, foreign office minister Mark Field said he would support revoking Article 50 – the two year process for leaving the EU – if it became an option in the event Mrs May’s deal was defeated and free votes granted for indicative votes.
What’s happening this week?
Monday: MPs will debate the Brexit next steps and a number of amendments – possible alternatives – to the government plan will be put to a vote. The most important of these is the indicative votes plan.
Tuesday: Theresa May could bring her withdrawal deal back for the so-called third meaningful vote. But the government says it won’t do that unless it’s sure it has enough support to win.
Wednesday: This is when indicative votes would be held – we don’t know yet whether MPs will be free to vote how they want or be directed along party lines. The chances of any genuine cross-party consensus being achieved are not high.
Thursday: A second possible opportunity for meaningful vote three. The prime minister may hope that Brexiteers will finally decide to throw their weight behind her deal because indicative votes have shown that otherwise the UK could be heading for the sort of softer Brexit they would hate.
Friday: This was the day the UK was meant to leave the EU. The earliest that will now happen is 12 April.
Read more on the week ahead in Parliament