Members of Theresa May’s cabinet believe she will have to resign this week should she allow a shift towards a soft Brexit, with angry Tory MPs examining ways to end her premiership.

The prime minister’s few remaining allies were engaged on Saturday night in a desperate battle to shore up her position, warning MPs that forcing May out would “tip the country into a general election and tear the party apart”. Downing Street is also warning hardline Tories that parliament is so against a no-deal Brexit the government would be brought down before it could implement such an outcome.

However, Tory MPs were this weekend examining ways of ousting May, and cabinet ministers on both sides of the Brexit debate made clear they were ready to quit if necessary.

Tory insiders described the party’s atmosphere as “end of days”. May was in her Chequers retreat on Sunday, talking tactics to colleagues.

On Saturday night the Conservative MP George Freeman, a former policy adviser to May, said: “I’m afraid it’s all over for the PM. She’s done her best. But across the country you can see the anger.”

I’m afraid it’s all over for the PM. She’s done her best. But across the country you can see the anger. Everyone feels betrayed. Government’s gridlocked. Trust in democracy collapsing. This cant go on. We need a new PM who can reach out & build some sort of coalition for a PlanB. — George Freeman MP (@GeorgeFreemanMP) March 23, 2019

May faces resignations from both wings of her cabinet should her Brexit deal be voted down this week, as expected. One of her team said they expected Brexit to come down to a “blunt choice between no deal or a customs union [with the EU]”.

Pro-Remain ministers will not tolerate any endorsement of a no-deal Brexit. But some pro-Brexit ministers have said that May could not carry on in No 10 unless she backed a no-deal Brexit. “It is being said that the only way she could stay on as prime minister is if she backed no-deal,” said a cabinet source. “That is where the party is – anything else would cause a huge division.”

David Lidington, the PM’s de facto deputy, would face opposition from hard Brexiters if he tried to succeed her. Photograph: Facundo Arrizabalaga/EPA

While accepting that May faces a terminal loss of support, some senior ministers are also warning that toppling her now would unleash a general election and a leadership fight that would be “toxic” for the Tories. “It is much better that one person is held responsible for all this mess,” said one senior minister.“If you get shot of her this week, you can almost guarantee an election and a whole set of problems.”

There is no clear plan of what would happen should May stand down. Some assume that her de facto deputy, David Lidington, would take over. However, seen as a pro-Remain minister, he would also face serious challenges from Tory MPs if he attempted to engineer a soft Brexit. One minister said: “The idea that everyone would step back and allow David Lidington to deliver a soft Brexit is absurd.”

There is a growing expectation among MPs that Downing Street will try to delay holding the next meaningful vote because of concerns that May would have to resign if she lost it for a third time. She had been expected to hold it early this week, should she be allowed to do so by the Commons speaker, John Bercow.

All options are being looked at by the prime minister’s team as they attempt to plot her survival through a perilous week. They are assuming that a plan by backbench MPs, led by the ex-cabinet minister Oliver Letwin, to hold a set of indicative votes on Brexit options will pass.

The prime minister has failed to deliver on her Brexit promise … she needs to announce a date for her departure Nigel Evans, Tory MP

One plan would see the meaningful vote held at the end of this week, should those indicative votes show that no other option could command a Commons majority. At the moment, several Tories are saying they believe May’s deal would be defeated by more than the 149-vote margin recorded at the second attempt. One government insider said: “There is a concern that we will go backwards.”

Requests for Theresa May to quit have been relayed to the prime minister and her team by both Sir Graham Brady, chairman of the backbench 1922 committee, and the chief whip. However, the decision has been taken to “face down” the calls.

Some Tory MPs are so exasperated with May’s leadership that they want to change party rules, enabling another vote to have her removed. Under current rules, a failed attempt to oust her last year means another vote cannot be held until December.

Former Tory minister James Duddridge tweeted: “Conservative MPs could have an indicative vote of no confidence in the PM. It would be a secret vote and we would get over 2/3 of MPs wanting her to go at least, likely lots more. If indicative votes are good for the Commons they are good for the Conservative Party. #Resign.”

One pro-remain Tory said that if May pressed ahead with a vote on her deal, it would be defeated and provoke “a new approach with a new PM”.

Sir Graham Brady, chairman of the 1922 committee, has been conveying requests to Theresa May for her to quit. Photograph: Leon Neal/Getty

Nigel Evans, executive secretary of the 1922 committee, said May needed, as a minimum, to announce a date for stepping down soon. “The prime minister has failed to deliver on her promise to the British people to deliver Brexit on 29 March,” he said. “It is her failure, and she needs to announce a date for her departure.”

Former Tory cabinet minister Nicky Morgan said May would have to quit if she failed to get her deal through parliament this week. “The PM has worked tirelessly, but her Brexit strategy hasn’t reached the conclusion she clearly expected it would. If the agreement is put to a vote this week and is defeated, then she will need to step aside to allow someone else to reset the strategy.”

Tory MPs say some of the prime minister’s closest aides in Downing Street have been hinting that May could try to call a snap general election if her deal does not get through the Commons for the third time, as she believes support for it is stronger in the country than in parliament.

But Conservative MPs have made clear to Brady that they would work together to block an early election. Under the Fixed-term Parliaments Act, two-thirds of the Commons would need to agree an early election.