Several times during the torrid Brexit drama of the past two years, Theresa May has adopted her own version of what Tony Blair used to call his “masochism strategy” – in her case by making herself available for hostile cross-examination by her backbenchers.

On Tuesday, though, as both wings of her deeply riven party erupted in fury and despair after the decision to ask for a three-month Brexit delay, she sent the ebullient Tory chairman, Brandon Lewis, in her stead.

Emerging from the meeting of the 1922 Committee, one MP said of his colleagues: “I wouldn’t say they were particularly happy.” Another was more blunt: “Terrible.”

And while they may have been deprived of the opportunity to say it to her face, May’s colleagues had spent much of the day speculating openly about how and when she could be persuaded to step aside.

One senior Tory MP from the soft-Brexit wing said he had “no words” to describe the gravity of the situation and believed May should go “now, immediately, this afternoon”. He said the view was “universal among Conservative MPs” that May should resign very soon as she had shown herself unable to lead in the circumstances.

“She is totally blown around by predictable events,” one frustrated backbencher said. “At some point she has to confront that her deal is dead. Parliament will simply not allow a minority government to overrule its no-deal decision. That would be an assault on our parliamentary democracy.”

Senior Eurosceptics were discussing ways to give May a “dignified exit” if her deal passes next week, perhaps by offering her another senior job if she promises to resign soon.

One influential European Research Group (ERG) MP, who voted against May’s deal last time, said there was now more of an appetite to support the withdrawal agreement, but May would have to make clear that she would go.

He said the idea of party grandees asking her to step down had been floated, with a promise that she would still have a role, such as a prominent ambassadorship, Lord President of the Council, or Tory leader in the House of Lords.

However May shows little sign of preparing to resign if her withdrawal bill passes, having promised Eurosceptics in conversations in recent days that she would change her negotiating team – including the Brexit secretary, Steve Barclay – in an attempt to prolong her premiership.

Instead, she dropped a heavy hint at the dispatch box on Wednesday that she might resign if her deal does not pass, necessitating a longer extension than the three months set out in the letter to the EU president, Donald Tusk.

“As prime minister I am not prepared to delay Brexit any further than 30 June,” she told MPs. Her spokesman refused four times to deny she would resign in that situation, instead repeating variations of the message, “what you are seeing is the extent of the PM’s determination to deliver Brexit”.

Dominic Grieve, who has known May since they were at Oxford University together, spoke for many in his party when he gave a stinging speech in the emergency Brexit debate, saying he had “never felt more ashamed to be a member of the Conservative party”.

He said the prime minister was “zig-zagging all over the place, rather than standing up for what the national interest must be” and if the government did not get a grip, “we will spiral down into oblivion – and the worst thing is, we will deserve it”.

In the corridors and tearooms, many others echoed his feelings, warning that while her central motivation has long been holding her party together, she has managed to please no one. Meanwhile, the Tories’ reputation is taking a daily hammering.

A plethora of ministers and even backbenchers are plotting a possible tilt at the leadership if “the ball comes loose from the scrum”, in the coming weeks and months, as Boris Johnson once put it.

More than a dozen Eurosceptics said May should resign at a meeting of the ERG on Tuesday night. But only a few Tories have publicly suggested she should resign since she fought off a no-confidence vote in December.

On Wednesday, Nigel Evans, the former deputy speaker, said there were “big questions” over May’s leadership as “trust is waning, ebbing away”.

Previously, Charlie Elphicke, the Dover MP, said he would support the withdrawal agreement if there was “a change of leadership, and a new face and a new team to take us forward to the future relationship”.

Nicky Morgan, a former education secretary, has suggested the cabinet may have to “take a role in saying potentially to the prime minister: ‘Actually, things have changed significantly. We think you should think about your position, prime minister.’”

May was attacked from both sides at PMQs, with the dogged Brexiters Peter Bone and Richard Drax castigating her for agreeing to any extension at all – while Labour MPs lined up to accuse her of failing to present any alternative plan.

Bone warned her: “If you continue to apply for an extension to article 50 you will be betraying the British people. If you don’t, you will be honouring their instruction. Prime minister, it is entirely down to you; history will judge you at this moment.”

Many of her colleagues appeared to have come to their own, damning judgment on Wednesday.