Britain’s foreign secretary and its chief Brexit negotiator caused quite a stir when they resigned within 24 hours of each other because they considered Prime Minister Theresa May’s Brexit proposal too accommodating to Europe. But if her government weathers the resulting storm, their departures could help resolve the tortuous divorce negotiations with the European Union, which are approaching crucial deadlines.

This crisis took shape after Mrs. May summoned her ministers to her official retreat at Chequers on Friday and hammered out what she called a “responsible and credible” proposal far short of the clean break she previously mooted. Though details are still to come, the plan would have Britain try to enter into a free-trade agreement with the bloc by a “common rule book for industrial goods and agricultural products,” and accept partial jurisdiction by the European Court of Justice.

Not surprisingly, Mrs. May’s chief Brexit negotiator, David Davis, a proponent of a “hard Brexit,” quit on Sunday, along with his deputy. The greater shock came on Monday, when the flamboyant foreign secretary, Boris Johnson, followed suit after declaring with typical cheek that selling the prime minister’s Brexit plan would be akin to “polishing a turd.” Mr. Johnson had been a fierce advocate of a total break with the European Union, and during the Brexit referendum campaign he notoriously spread the false claim that Britain would save more than 350 million pounds a week if it left the union.

The resignations immediately set off speculation about more defections, the potential fall of Mrs. May’s government and even new elections. All that could happen. But it is doubtful that hard-line Brexiteers in Mrs. May’s Conservative Party can muster the 48 votes that party rules require to force a vote of confidence, much less the votes needed to force her into a leadership contest (in which Mr. Johnson would be a potential candidate).