He has a few things going for him, chief among them a divided opposition. The left-wing Labour Party, led by Jeremy Corbyn, has always wanted to keep closer economic ties to the E.U. and is now backing a second Brexit vote. But the Liberal Democrats, a smaller centrist force, are wary of ousting Mr. Johnson because they don’t want Mr. Corbyn as prime minister.

Still, the situation is fluid and the math is tight, so the votes this week could go either way.

Conflicting signals: Late on Saturday night, after Parliament’s vote, Mr. Johnson sent two letters to the E.U. — one formally asking for an extension, which he left unsigned, and a signed letter saying that another delay would “damage the interests of the U.K. and our E.U. partners.” It is now up to the E.U. to decide how to respond.

The view from Brussels: E.U. officials who once expressed hope that Britain would somehow end up remaining in the bloc now just want the country to leave already so that they can move on to other pressing issues.

Order! Order! The Speaker of the House of Commons, John Bercow, who decided to allow the vote on Saturday that derailed Mr. Johnson’s plans, will soon be stepping down. The hunt is on for his replacement.