Lee Rowley, another Conservative lawmaker, reminded the prime minister of words she had spoken last week, when she said Mr. Corbyn was “the biggest threat to our standing in the world, to our defense and to the economy.”

“In her judgment,” he continued, “what now qualifies him for involvement in Brexit?”

The rumblings from Tory Brexiteers were ominous all day. Two ministers resigned in protest over the talks between Mrs. May and Mr. Corbyn, one sputtering his outrage that “you and your cabinet have decided that a deal — cooked up with a Marxist who has never once in his political life put British interests first — is better than no deal.”

Then Mrs. May and Mr. Corbyn vanished into a room with their teams, and, shortly thereafter, a great thunderclap split the air above Westminster.

There was nothing to do but wait.

“Will they put party before country? Or country before party?” asked Rob Ford, a professor of political science at the University of Manchester. “There was always going to come a moment when the irresistible force of tribal partisan loyalties and distrust of the opposition came up against the immovable object of a no-deal Brexit deadline.”

“If they don’t do something,” he added, “they’re all going down together.”

By compromising, each runs the risk of inflicting permanent damage on their fragile parties, which are both deeply split over Brexit. And one thing they have in common is that their entire adult lives have been spent serving their parties.

Mr. Corbyn, who grew up in the prosperous and conservative Wiltshire countryside, was one of the few boys in his school to sign up with the Young Socialists, Labour’s youth wing, at 16. Mrs. May began working for the Conservative party before she was a teenager, spending weekends with Tory matrons stuffing envelopes and delivering fliers.