The Prime Minister is being warned that a Tory grassroots revolt will take place next month if she does not set out specifics on when she will pack her bags and leave Downing Street.
The pressure on her position continued to mount as an official announcement about her failure to avoid European elections was quickly followed by continuing deadlock over Brexit talks with Labour.
A Tory showdown will take place today as Sir Graham Brady, chairman of the 1922 committee of backbench MPs, reveals the outcome of his secret departure talks with Mrs May to his colleagues.
Sir Graham has faced angry calls from backbenchers for "clarity" on Mrs May's timetable for standing down and triggering a leadership contest.
The treasurer of the 1922 Committee, Sir Geoffrey Clifton-Brown, said he would back a grass roots bid to force Mrs May out with a no-confidence vote next month if she did not go of her own volition.
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The Tory MP for the Cotswolds said it was the Prime Minister's decision on when she should go but he would "absolutely" support grass roots moves to try to topple her in June if her departure date was not imminent.
When asked what should happen if Mrs May failed to set out her own timetable for departure, he said: "It begins to get much more messy.
"It would be much easier and I think the European elections would be much easier if she did set out her own timetable to go but it is up to her.
"I think it's quite possible they (grass roots members) might vote for no-confidence in June.”
Senior Tory activists will consider the question of Mrs May's leadership at an emergency meeting of association chairmen - set for Saturday, June 15.
Tory MPs are powerless to remove Mrs May following a failed bid to boot her out as leader in December last year, led by Tory MP Jacob Rees-Mogg - but the grass roots are calling for a rule change.
The vote by members at an EGM of the National Conservative Convention would not be binding but would add pressure on Mrs May to quit if passed.
In a message to members of the convention, reported by the Conservative Home website, chairman Andrew Sharpe said they would be asked to vote on a motion stating "we no longer feel that Mrs May is the right person to continue as Prime Minister to lead us forward in the negotiations" and "therefore with great reluctance ask that she considers her position and resigns”.
Dinah Glover, a Tory activist whose petition triggered the EGM, told the i newspaper: "The party at the moment is in absolute meltdown because they are terrified she is going to do a deal which will do damage to our country.”
The news of more threats came as Mrs May officially accepted she cannot get her Brexit deal through Parliament in time to avoid European elections on May 23.
Her effective deputy David Lidington confirmed the elections will go ahead, but said the Government was "redoubling our efforts" to get an EU Withdrawal Agreement ratified by the start of July so the MEPs elected this month never have to take their seats.
Only hours later, shadow business secretary Rebecca Long-Bailey confirmed negotiations on a new Brexit deal that could win a parliamentary majority have still to bear fruit.
"Nothing has been agreed yet," she said after a three-hour meeting, which she labelled "very robust”.
But Ms Long-Bailey said there had been no movement towards a customs union, temporary or otherwise, and would only say another referendum was "one of many options”.
She said: "We haven't had any movement or agreement on a customs union, certainly not today, but we will see what the rest of the week holds.
"Our policy position has not changed since the last Labour conference, where a public vote was one of many options on the table, certainly to avoid a Tory deal, a bad Tory Brexit or a no-deal situation.
"Certainly we've been exploring the issue of a confirmatory vote in these discussions, but as yet nothing has been agreed.”
A Downing Street spokesman added more talks were scheduled for Wednesday.