But her outreach to Labour represented a shift in strategy after months trying to woo hard-liners in her own Conservative Party. And she indicated that in determining the future relationship between Britain and the E.U., she might be willing to countenance the softer Brexit that Labour leader Jeremy Corbyn says he supports.

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In a brief TV statement, May offered to hold talks with Corbyn “to break the logjam.”

The two leaders share a chilly, almost disdainful relationship. As recently as Monday, Corbyn was calling for a general election.

On Tuesday, Corbyn said he would be “very happy” to meet with the prime minister. “We recognize that she has made a move,” he told Sky News. “I recognize my responsibility to represent the people that supported Labour in the last election and the people who didn’t support Labour but nevertheless want certainty and security for their own future, and that’s the basis on which we will meet.”

According to May’s plan, if she and Corbyn can hammer out a compromise, the government would then present it to the House of Commons for a vote.

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If a deal between the two leaders proves impossible, May said, she would offer Parliament a number of Brexit options, with the government committed to enact the plan that could win a sustainable majority.

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The aim, she said, would be to leave the E.U. with an approved deal by May 22. But if the gamble fails, Britain could be headed for a chaotic no-deal departure in the coming months.

“This is a difficult time for everyone,” May said. “Passions are running high on all sides of the argument, but we can and must find the compromises that will deliver what the British people voted for.”

E.U. leaders had given her until April 12 to propose a plan for Brexit or face leaving the continental trading bloc without a deal and without the safety net of a two-year transition period.

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Her proposal now depends on the willingness of E.U. leaders to extend her a lifeline next week. After her statement, European Council President Donald Tusk called for patience.

But plowing forward without organizing late May elections for the European Parliament sends Britain down a path of no return. European leaders have said they are unwilling to tolerate Britain remaining in the E.U. beyond the end of June if no elections are held. Some leaders may even demand that May start election preparations, just in case, as a condition for a brief extension.

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Although they have bent in the past, European diplomats say the end of June date is a bright red line they will not cross.

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The Europeans would probably hesitate to force Britain out if it appeared to be searching for ways to have a closer relationship with the bloc.

A customs union — one of the plans that May and Corbyn might be able to agree on — would be an off-the-shelf plan that Europeans could arrange within days, negotiators say. Some joke that if the right people are sitting in the room, they could fix it up in an afternoon.

May’s offer to negotiate with Corbyn came on the day that a cross-party group of lawmakers tabled a bill that would require her to seek an extension beyond the April 12 deadline. The bill, which will be voted on Wednesday, aims to stop a “no-deal” Brexit.

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Any compromise May could reach with Corbyn might be left for her successor to execute. Last week, she promised Conservative lawmakers that if her withdrawal deal goes through, she would resign before the future-relationship negotiations with Europe.

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Boris Johnson, Britain’s ambitious former foreign secretary who would be a top contender to replace May, tweeted on Tuesday: “It is very disappointing that the cabinet has decided to entrust the final handling of Brexit to Jeremy Corbyn and the Labour Party.”

Johnson added, “It now seems all too likely that British trade policy and key law making powers will be handed over to Brussels — with no say for the U.K.”