Brexit is tearing British society and its political classes apart as the sides devolve into warring tribes of “leavers” and “remainers,” neither with enough power to best the other.

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“I think it’s astonishing she is carrying on as prime minister,” said Jonathan Tonge, a politics professor at the University of Liverpool. “Not just because of the size of the defeat, but also because she told us that this was the ‘best and only deal.’ So, by definition, any course she pursues now is an inferior course.”

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May now must return to Parliament on Monday to present lawmakers with some sort of Plan B for exiting the 28-member union. Yet the deep disagreements over how and whether Britain should leave the European bloc persist.

In Brussels, European diplomats said that the onus was on British lawmakers to come up with a proposal — any proposal — that could win a majority in Westminster, so that there could be a basis for continued talks between the sides in Brussels. European leaders expressed impatience — and growing dread — that Britain was rushing toward the edge of the Brexit cliff on March 29 with no safety nets in place.

In brief remarks outside her official residence at 10 Downing Street, May said she understood if people outside Parliament found the previous 24 hours “unsettling.”

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“Now MPs have made clear what they don’t want, we must all work constructively together to set out what Parliament does want,” she said, adding that she had invited the leaders of all parties to meet with her to try to hammer out a deal that could pass a bitterly divided House of Commons.

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Opposition Labour Party leader Jeremy Corbyn, who initiated the confidence motion against the government, had so far refused her overture, May said.

Labour leaders insisted that May first rule out a “no-deal” Brexit, which they say would wreak havoc in Britain.

“Before there can be any positive discussions about the way forward, the government must remove, clearly and once and for all, the prospect of the catastrophe of no-deal and all the chaos that would come as a result of that,” Corbyn said.

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Leaders of the Scottish National Party have been in discussions with May this week but said that avoiding a no-deal Brexit, extending the deadline for leaving the E.U., and consideration of a second Brexit referendum “have to be on the table” as options.

May said again in Parliament on Wednesday that she would not support a second referendum.

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Within May’s Conservative Party, too, factions have put down markers.

The hard-line wing of Tory Brexiteers published a plan Wednesday for leaving the E.U. with no deal and trading with Europe as a third country.

Although a third of Conservative Party members on Tuesday voted against the withdrawal agreement May negotiated with European leaders, and even though Conservatives challenged her leadership in a party-only confidence vote just last month, Conservatives supported her in the confidence vote involving the whole House of Commons on Wednesday.

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Tim Bale, a politics professor at Queen Mary University of London, said May is still standing, in part, because no one else in her party wants to take over at the Brexit helm.

“Who else is there? Who wants to take on this role?” Bale said. “No hard Brexiteer wants to, because they know, in their heart of hearts, it can’t be done and they don’t want to be blamed for it. And anyone else would have to come from a soft Brexit perspective and would end up splitting the party.”

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Besides not having an obvious leader waiting in the wings, the Tories do not want a general election against Labour.

The sparring between the parties during the day-long debate over May’s fate on Wednesday was punctuated by withering rhetoric and sharp thrusts.

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Tom Watson, the deputy leader of the Labour Party, was somber but gripping: “432 to 202,” he said, citing the result of the vote in which May’s Brexit plan was defeated. “Mr. Speaker, that is not a mere flesh wound.”

“No one doubts her determination, which is generally an admirable quality,” Watson said of May. “But, misapplied, it can be toxic.”

Conservatives sought to turn the tables with a rip-roaring speech from Michael Gove, the environment secretary. Gove laid into Corbyn: “He wants to leave NATO. He wants to get rid of our nuclear deterrent. And recently in a speech he said, ‘Why do countries boast about the size of their armies? That is quite wrong. Why don’t we emulate Costa Rica that has no army at all?’ No allies. No deterrent. No army. No way can this country ever allow that man to be our prime minister.”

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The Conservative benches roared with delight.

For his part, Corbyn said May was running a “zombie government,” raising the specter of the undead prime minister repeating over and over again that “Brexit means Brexit” while devouring the brains of her party.

“Brexit is like a black hole that devours all light,” Labour’s Angela Eagle said.

Phillip Lee, a Conservative Party member who resigned as a minister because he opposed May’s deal, asked the prime minister whether she accepts that she may now have to change her approach to Brexit.

May did not say yes, but she did not say no.

Nicola Sturgeon, leader of the Scottish National Party, told the BBC that she spoke with May after the defeat of her Brexit bill. Sturgeon said, “To be perfectly frank, I didn’t glean very much — she was at pains to tell me she wanted to sit down with other parties and listen to other ideas. But I got the very strong sense she does not have a clear idea herself of what the next steps are, and it doesn’t seem to me as if she is prepared to abandon or move any of her red lines to open space for new approaches to be brought forward.”

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Sturgeon added, “It sounded like what she wanted to do was find a minor variation of her current deal — the one that was so overwhelmingly rejected last night.”