Under the Conservative Party’s current rules, its members of Parliament can hold a binding vote of no confidence in Mr. Johnson if 54 of them write to formally request one. The request letters are confidential.
So far only four Conservatives in Parliament have publicly called on Mr. Johnson to quit. Only one senior lawmaker knows how many have written letters, and he would only make the number public if it reached the threshold for a challenge.
In a no-confidence vote, held by secret ballot, Mr. Johnson would keep his job by winning a simple majority of Conservative lawmakers. He would then be safe from another such challenge for a year unless the rules were changed.
His cabinet could fatally undermine him.
Cabinet rebellions destabilize prime ministers and can prove crucial in pushing them toward the exit. The catalyst for Margaret Thatcher’s demise in 1990 was the resignation of Geoffrey Howe, a disaffected former ally, and Theresa May lost several ministers — including Mr. Johnson himself, who quit as foreign secretary in 2018.
As prime minister, Mr. Johnson has more or less maintained cabinet discipline so far. But one senior minister, the former Brexit negotiator David Frost, quit late last year, citing policy differences. And it took several hours for Rishi Sunak, the chancellor of the Exchequer, to express lukewarm support for Mr. Johnson after his apology. Of course it might just be a coincidence, but Mr. Sunak is a leading contender to take over if Mr. Johnson falls.