On Thursday, in order to break the impasse and shape a Brexit plan that might pass a spectacularly divided Parliament, May held meetings with leaders of opposition and independent parties at 10 Downing Street.

Briefing reporters, her official spokesman — who goes unnamed according to protocol — promised that the talks would be undertaken “in a constructive spirit,” but he was also clear that May was not prepared to budge on any of the main issues that led lawmakers to reject her 585-page Brexit withdrawal agreement.

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No, May was clear, she would not support a second referendum, which is what Brexit opponents want, according to the spokesman. ITV News reported that opposition lawmakers were given a paper by the government that contended that staging another Brexit referendum would take a year to organize.

Nor would the prime minister endorse permanently joining a European customs union — which is what those who want a softer Brexit seek — because, her spokesman said, it would then be difficult or impossible to seek free-trade deals with other countries, such as the United States.

Nor would May promise to take off the table the option of leaving the E.U. with no deal March 29, which is what the Labour Party wants to hear.

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And finally, no, the prime minister would not ask European leaders to delay Britain’s departure beyond the March date — by extending or revoking the E.U. Article 50 — as the Scottish National Party has demanded as a condition of further talks.

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Why? “Because we do not wish to do it,” May’s spokesman said.

In a speech Thursday, the leader of the opposition Labour Party, Jeremy Corbyn, called May’s invitation to talk a “stunt.”

“If you are serious about reaching a deal, then ‘no deal’ must be ruled out,” Corbyn wrote to May.

The Labour leader warned that, although he had lost round one, he was prepared to bring forward more motions to try to topple the government in coming days.

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“The government may have survived a confidence vote — for now,” Corbyn said. “But we have a government in name only.”

But just as May’s Conservative Party is tearing itself apart over Brexit — divided by hardcore Brexiteers who just want out and those who want either a soft Brexit or no Brexit at all — Labour is riven by similar splits between “leavers” and “remainers.”

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Mike Gapes, a Labour lawmaker and critic of Corbyn’s, tweeted: “Apparently Corbyn is prepared to hold talks with Hamas, Hezbollah, [Syrian President Bashar al-]Assad and Iran without preconditions. But not with the UK Prime Minister. Why?”

Reporters camped out at 10 Downing spotted a half-dozen Labour Party backbenchers going into the cabinet offices to talk with May’s ministers about breaking the Brexit logjam.

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Former prime minister Tony Blair, of Labour, said Corbyn must meet with the British leader. Speaking to the BBC, Blair said: “In a moment of a national crisis, the prime minister asks the leader of the opposition to talk? Of course you go and talk.”

And no matter what May’s negotiating position is now, Blair said seeking an extension to Article 50 — to delay Brexit beyond March — is “inevitable.”

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If he were in government, Blair said, “I would already be having discussions with Europe about the terms of extension.”

The government insists that Britain is leaving at the end of March. May’s office said she would be skipping next week’s World Economic Forum meeting in Davos, Switzerland, to focus on the Brexit crisis.

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Caroline Lucas, the Green Party’s lone member of Parliament, met with May and told reporters the prime minister resisted the option of delaying Brexit and extending Article 50.

The idea of hitting the pause button is gaining momentum in Parliament. But time is running out. Any extension would need the unanimous agreement of all 27 remaining E.U. countries.