Prime Minister Theresa May is expected to update ministers on her Brexit strategy as 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”.
Meanwhile, the EU has said it is “increasingly likely” the UK will leave without a deal on 12 April.
Conservative MP Nigel Evans told BBC Radio 4’s Today programme that Mrs May should get her deal over the line, and then resign.
Mr Evans, a joint executive secretary of the influential 1922 Committee of backbench Tory MPs, 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.”
International Trade Secretary Liam Fox told BBC Breakfast the government was “constrained by the fact that we have a leave electorate and a Parliament that leans towards remain and the government doesn’t have a majority in the House of Commons”.
“Changing the prime minister doesn’t change any of that basic arithmetic,” he said.
Work and Pensions Secretary Amber Rudd said she was “still committed” to working with the prime minister to get her deal through and this was “the best way to end this chaos”.
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 was 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.
Later 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.
The indicative votes are a process for MPs to indicate which version of Brexit they might like if they don’t fancy the prime minister’s deal.
But there’s a clash in government over whether or not they should go into this process at all.
Parliament is going to do this anyway and the government has given a commitment for MPs to be able to have their say on a series of different ideas.
To be clear, it would not bind the government – even if there is one option that gets a clear preference from Parliament.
It would still have to get through the cabinet and it would still have to be workable for the Tory party.
That could then mean if Parliament puts down a marker to have a softer Brexit, Theresa May is stuck with the same problem she’s had all along: if she moves to something softer she might implode the Tory party.
Quite openly now, people in government are talking about something more dramatic as a way out.
Cryptically they call that a “democratic event”. What would we call that? An election.
Conservative MP Sir Oliver Letwin told the Today programme that once Mrs May knew 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 they are in favour of, though he would not confirm whether Tories would be given a free vote on the options.
Mr Fox told the Today programme that there had to be an agreed deal by 11 April, otherwise the UK will have to take part in EU elections, which “would unleash a torrent of pent up frustration from voters”.
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.
Labour MP Wes Streeting said he believed there to be a “genuine desire” to find a way through the deadlock “but the prime minister has to set Parliament free”.
And Labour MP Peter Kyle said “what the country really wants” is for “grown ups to get a grip on this and show a creative and a solid way out of the madness”.
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.