Theresa May is to hold talks with the 1922 committee of backbench Conservative MPs on Thursday.
As MPs they are demanding to know exactly when she will leave Downing Street.
Sir Geoffrey Clifton-Brown, committee treasurer told the Press Association, “It would be infinitely preferable if she set a date rather than us force her out.
“It’s better that she does it than we have a vote of confidence.
“What I would like to see is her set out a timetable to trigger a leadership contest.”
Andrew Bridgen, Conservative MP told the Press Association, “I would like to see the 22 give her a timetable to stand down.
“And, if she does not accept that timetable, tell her we will have another vote of confidence after the European elections.”
Currently there cannot be a vote of no confidence in May’s leadership until December.
However, according to sources the 22 committee will be holding a private meeting to discuss Tory leadership contest rules.
Mark Francois, a prominent Brexiteer has predicted a poor Conservative showing in next week’s European Parliament elections.
Francois told the Press Association, “As the polls increasingly suggest, we are going to have an extremely difficult night in the European elections.
“And, because they are announced on a council by council basis, every MP will be able to reverse engineer the result in their own constituency.
“At that point, I believe, my colleagues will finally wake up and smell the coffee if they have not, indeed, done so already.”