If she were to lose that, then Conservative lawmakers would choose two candidates, with the final vote going to party members (who tend to be older, more right-wing and pro-Brexit).

But getting rid of Mrs. May would be “extremely hard,” said Tim Bale, a professor of politics at Queen Mary University of London.

“If you were to say to Conservative members of Parliament, ‘Would you like two months of leadership contests, exposing all the divisions in the party in full public gaze in the middle of the most vital negotiations in recent times?’” said Mr. Bale, “I think most would rather say ‘No.’”

On top of that, because a full-blown leadership contest would be likely to yield a Brexit hard-liner like Mr. Johnson, lawmakers who want a pragmatic Brexit would probably side with Mrs. May. Brexit enthusiasts might fear that a candidate who is more pro-Europe than Mrs. May could sneak through.

Even if Mrs. May were pushed out, Mr. Johnson would have to worry not just about Mr. Javid but also about rival hard-line Brexit supporters, including Mr. Rees-Mogg and Michael Gove, the environment secretary, as well as more moderate contenders (perhaps as many as 20, according to the London Sunday Times.)

This range of options presents another dilemma for the Conservative Party: Replace Mrs. May now with someone who might be a tougher Brexit negotiator, or wait and choose someone with a better chance of winning the next election, scheduled for 2022.

“You might feel that Gove is up for negotiating a much better deal, but if you did that it’s hard not to keep him for the next election and there is no evidence that he will capture the hearts and minds of voters,” said Mr. Gimson, who noted that Mr. Johnson’s fortunes are currently in “eclipse.”