The leaders seized hold of the Brexit process when May after repeated questioning proved unwilling, or perhaps unable, to tell them what she planned to do next week if she fails yet again to convince a skeptical British parliament to endorse the deal, European Union officials said.
As Downing Street rubbished reports that May could be persuaded to resign, chancellor Philip Hammond told Sky News on Sunday: "This is not about the prime minister. changing prime ministers wouldn't help, changing the party of government wouldn't help".
"At first she appeared to be a unifier, but she turned out to have too little courage, imagination or skill to lead the Brexit negotiations", said a recent editorial in the Conservative-backing Spectator magazine.
Still, Mrs May has been unable to generate enough support in Parliament for the deal her Government and the European Union reached late past year.
Failing that, they gave May until April 12 to choose between leaving the bloc without a divorce deal or deciding on a radically new path, such as revoking Britain's decision to leave, holding a new referendum on Brexit or finding a cross-party consensus for a very different kind of Brexit.
After another turbulent week for the Prime Minister which saw her come under fire for delaying Brexit and seeking to blame MPs for the impasse, the Commons was expected to be given the third chance to vote on her Withdrawal Agreement this week.
She also faces pressure from groups demanding a second Brexit referendum. While many parliamentarians have lost faith in May to deliver on Brexit, senior members of her cabinet are dismissing reports that a cabinet coup is in the works.
Now a departure date of 22 May will apply if parliament rallies behind the prime minister and she is able to pass her deal.
But he said her inability to engage with colleagues had exacerbated divisions over Brexit, describing her as "the living embodiment of the closed door".More news: Limerick Parcel Appears Identical To Those Sent To UK
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The newspaper cited 11 unidentified senior ministers and said they had agreed that the prime minister should stand down, warning that she has become a toxic and erratic figure whose judgment has "gone haywire".
Also in attendance was Cabinet Office minister David Lidington, who as deputy to Mrs May is tipped as a potential caretaker PM if she is forced to quit to save the deal.
"I think (she) is doing a fantastic job", Lidington said.
The proposal seeks to pave the way for a series of indicative votes in the Commons on Wednesday, effectively taking control of the Brexit process out of the hands of the Government.
Conservative Party legislator George Freeman, a former policy adviser to Mrs May, tweeted that the United Kingdom needed a new leader if the Brexit process was to move forward.
Following last week's delay to the country's March 29 scheduled departure - which MPs must still vote into law this week - the way forward remains highly unpredictable.
He wrote today: "I'm afraid it's all over for the PM". "She's done her best".
The push for second referendum gained momentum over the weekend with with over a million people joined the "Put It To The People" March in London.
"The Labour Party, as you know, like the country, was split". "Everyone feels betrayed", Freeman tweeted. They have twice down-voted May's deal, they have rejected a no-deal Brexit, they didn't dare clearly support a second referendum nor had they the courage to altogether abolish Brexit, despite there being a majority for that.
At one of the most important junctures for the country in at least a generation, British politics was at fever pitch and, almost three years since the 2016 referendum, it was still unclear how, when or if Brexit will ever take place.