Jacob Rees-Mogg has warned fellow Tory MPs that if they don’t ditch Theresa May now she will lead them into the next election, scheduled for 2022.
Few Tories thought this was a “good idea”, the Brexiteer MP suggested.
Mr Rees-Mogg wants to oust the PM over her EU withdrawal agreement but has so far failed to get enough colleagues to back his call for a no confidence vote.
The cabinet met earlier for the first time since two of its members quit over the draft Brexit deal.
Chief Whip Julian Smith said the three hours of ministerial discussions had been “positive”.
He said it was going to be a “really exciting” week as Mrs May headed to Brussels for talks with European Commission President Jean-Claude Juncker ahead of a crunch Brexit meeting of EU leaders on Sunday, which is expected to sign off on the withdrawal agreement.
A group of Brexiteer cabinet ministers, headed by Commons leader Andrea Leadsom, have been pushing for changes to the draft withdrawal agreement, to get rid of the Irish “backstop” plan, which has led to claims the UK will be tied to the EU indefinitely.
Downing Street said the cabinet had discussed possible alternative arrangements to keep the border open, that could involve “technological solutions”.
Asked if parts of the withdrawal agreement could be re-negotiated, Chief Whip Julian Smith said: “There’s a focus on getting the deal done.”
But, in a sign of tension on the EU side, Spain has said it will not agree to the draft Brexit withdrawal deal without clarity over how talks on the future status of Gibraltar should be handled.
Ministers from the remaining 27 EU countries have met in Brussels to work on the political declaration setting out their future relationship with the UK, which could be agreed with the UK later on Tuesday.
Mr Rees-Mogg said he had not given up hope of getting the 48 letters of no confidence in the PM needed to trigger a vote.
“What we are seeing from this government is a deliberate decision not to deliver a proper Brexit,” he told reporters at a Westminster news conference.
“We have a government led by Remainers who want to keep us tied into the EU as tightly as possible.”
He said the 48 letter threshold might be reached next month when MPs get a “meaningful vote” on the withdrawal agreement.
But he added: “I think it is now, or the prime minister will lead the Conservatives into the next election.
“You find MPs privately who will say to you that they think that is a really good idea in any number and I would be quite surprised.”
Mrs May’s allies insist she would win a no confidence vote and under Conservative rules she would then be immune from a challenge for 12 months.
The PM says her Brexit deal is the best the UK can get from Brussels and will allow the country to take back control of its “money, laws and borders”.
Downing Street said that, during talks with Scotland’s First Minister Nicola Sturgeon, the PM had emphasised that the draft Brexit terms would give Scottish businesses the “clarity and certainty they need to protect jobs and living standards and see us take back control of our waters, improving the fortunes of our fishermen”.
The SNP leader earlier met Labour leader Jeremy Corbyn to discuss tactics ahead of the Commons vote.
Ms Sturgeon held a separate meeting with Lib Dem leader Sir Vince Cable, Green MP Caroline Lucas and Plaid Cymru’s Westminster leader Liz Roberts, who all back another EU referendum.
She told the BBC’s Laura Kuenssberg she wanted to form a “coalition of opposition” to Mrs May’s Brexit plans, and that momentum for another referendum was growing.
She described her talks with Mr Corbyn as “exploratory” and she did not know whether he would back a referendum.
But she said they had both agreed that the PM’s Brexit deal is a bad one and that no-deal should not be the only alternative presented to MPs.
“The next stages of all of this have to be to look at what we can coalesce around in terms of alternatives,” she told Laura Kuenssberg.
A Labour spokesman said: “They discussed their common opposition to Theresa May’s botched Brexit deal and determination to work across Parliament to prevent a disastrous no-deal outcome.”
The Labour leader has said his preferred option is a general election and a referendum was “not an option for now”.
As it stands, there appears to be a majority in Parliament against the deal.
The prime minister is also coming under pressure from the Democratic Unionist Party, whose 10 MPs keep her government in power.
The DUP abstained in Monday night’s Budget votes as a warning shot over what they say are her broken promises on Brexit – and the BBC understands they will do the same in Tuesday night’s votes.
Under the terms of their House of Commons deal, agreed after Mrs May lost her Commons majority in last year’s general election, the DUP is supposed to back the government on Budget matters and on confidence votes.
The DUP has said Mrs May’s Brexit agreement with Brussels breached a “fundamental” assurance that Northern Ireland would not be separated from the rest of the UK.
The party’s deputy leader Nigel Dodds said: “The government will require DUP support to deliver its domestic agenda. We will continue to use our influence for the good of everyone across the United Kingdom.
“If the government can look beyond a withdrawal agreement, which is uniting people from across the political spectrum against it, and instead work towards a better deal, then an outcome can be delivered that truly works to benefit all parts of the United Kingdom.”
Labour’s shadow cabinet office minister Jon Trickett said the DUP’s withdrawal of support on a Budget measure raised questions as to how long the government could carry on in the face of widespread opposition to Mrs May’s Brexit deal.
“We no longer have a functioning government. With Brexit only a few months away something has got to give,” he said.
The DUP opted to abstain on a series of amendments to the Finance Bill – and also supported an amendment proposed by Labour, calling for Treasury assessments of the impact of government policies on child poverty to be published.
Labour’s celebrations were somewhat muted, however, as they had not been expecting the DUP to vote with them and did not have enough of their own MPs on hand to win the knife-edge contest, losing it by five.
Labour leader Jeremy Corbyn, who had put forward the amendment himself, was among the absentees, having been given permission by his party’s whips not to vote.