Theresa May will today meet with senior Tories, who are demanding she sets a firm resignation date.
The Prime Minister is holding talks with members of the executive of the 1922 Committee of backbencher, as pressure mounts on her to make clear when she will exit Number 10 grows.
But Committee treasurer, Sir Geoffrey Clifton-Brown, said they would not be afraid to "force her out" if necessary.
"It would be infinitely preferable if she set a date rather than us force her out," he said.
"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."
After the talks with the Prime Minister, the 1922 Committee executive will hold a private meeting where changes to Conservative leadership contest rules could be discussed, according to sources.
At present, Mrs May cannot be challenged again as leader until December.
The meeting with the Tory grandees follows Mrs May's announcement that the Withdrawal Agreement Bill will be brought to the Commons for a fourth time in early June.
The Prime Minister said: "When MPs come to look at this Bill, when they come to vote on this legislation, I'm sure that they will be thinking of the duty that we have to ensure that we deliver on the vote of the British people."