LONDON — Two weeks before Britain was originally scheduled to leave the European Union, Jeremy Corbyn, the leader of the opposition Labour Party, was asked on television whether Britain should stay or go. He refused to answer.

The question came again, and again, and again, and then one last time. He still refused to answer.

“I want us to have a serious relationship with the E.U.,” he said, gliding past the in-or-out question that has consumed Britons for the better part of three years.

But now, with the Conservative government and Labour in talks to devise a deal they can both support, and with yet another deadline looming, Mr. Corbyn’s tightrope walk may be near an end.

Until now, his studied ambiguity has largely held his party together while the Conservatives have crumbled. But having accepted Prime Minister Theresa May’s offer to negotiate, he will likely face uncomfortable choices if Mrs. May softens her stance and tries to tempt him with a credible compromise.