A visibly frustrated May said she would seek only a short extension, until June 30. If the delay were longer, Britain as a member of the E.U. would have to participate in upcoming elections for the European Parliament.

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A longer delay would also provide “endless hours and days of this House carrying on, contemplating its navel on Europe,” May charged, underscoring her contention that Parliament, not her government, is responsible for the chaos.

“The British people deserve better than this House has given them so far,” she said.

The prime minister’s cutting remarks were met with hoots and jeers, even by members of her Conservative Party, whose rebels have not only voted against her Brexit plan but tried to unseat her.

Many lawmakers blame May for the shambles of Brexit, accusing her of weak leadership, a failure to seek consensus early on — and a bad deal they fear could yoke Britain to E.U. rules and regulations forever.

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In the evening, the prime minister doubled down. She stepped to the lectern at 10 Downing Street to talk directly to the people — and point the finger again.

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“You, the public, have had enough,” she said. “You are tired of the infighting. You are tired of the political games and the arcane procedural rows. Tired of MPs talking about nothing else but Brexit when you have real concerns about our children’s schools, our National Health Service and knife crime. You want this stage of the Brexit process to be over and done with. I agree. I am on your side.”

In a letter delivered Wednesday to Donald Tusk, the president of the European Council, May wrote that she was “confident” the House of Commons would eventually pass a tweaked withdrawal agreement, but not by March 29, when Britain is scheduled to leave the E.U.

May will now travel, hat in hand, to a summit of skeptical European leaders in Brussels on Thursday. This will mark at least the 17th time the gathering has been forced to discuss Brexit since the June 2016 referendum.

The French, for their part, appear exasperated by Britain’s dithering.

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“The central scenario is a no-deal exit,” French Foreign Minister Jean-Yves Le Drian announced Wednesday, making clear his government’s hard-line approach.

“We are ready,” he said.

But at a later news conference in Brussels, Tusk said that “a short extension will be possible, but it will be conditional on a positive vote on the withdrawal agreement in the House of Commons.”

Meaning: The Europeans do not want to give May the delay until the deal is inked.

Brussels officials cautioned that May’s last-minute letter asking for more time probably arrived too late for European leaders to respond to it definitively Thursday. Leaders need to consult with their cabinets and parliaments, policymakers said.

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That sets up the likelihood of a nail-biting, last-ditch emergency summit next week.

In briefings, diplomats from several European countries made clear they would do everything they could to avoid having Britain leave without the safety of a withdrawal agreement. “We will go to great lengths to avoid a hard Brexit,” one senior E.U. diplomat said, speaking on the condition of anonymity to offer a frank assessment.

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The British prime minister is struggling to persuade 10 members of the Democratic Unionist Party of Northern Ireland, which props up her minority government, to back her deal. The thinking is that if the DUP swings behind her, some hardcore Brexiteers in her own party may hold their noses and support her plan.

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May told Parliament that even if an extension is granted, a “no-deal Brexit” wasn’t off the table. Instead, the cliff edge would simply be pushed back.

That alarmed some lawmakers who think exiting the bloc without a deal would be economically disastrous for the country. Samuel Gyimah, a ­Conservative lawmaker, told the BBC that a short extension “increased chances of a ‘no deal’ by 60 percent” and that it was “downright reckless” of the government to keep it as an option.

British reporters were told by 10 Downing Street that May might try to pass a revised deal as early as next week. But the prime minister faces procedural head winds, as well as political ones. The speaker of the House of Commons, John Bercow, ruled Monday that he would not let May bring a recycled plan back for a third vote unless it is “substantially” different.

In Brussels, astonished diplomats increasingly expect that an extension will not be decided on until the hours before March 30.

Although people involved in the negotiations said Wednesday that there was little appetite for ejecting Britain against its will, they were fearful that further surprises in London could lead to what one senior E.U. diplomat called “catastrophe.”

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“All we have done, leading to nowhere,” the diplomat said, speaking on the condition of anonymity to discuss calculations ahead of the meeting Thursday. “The blame game will be a very nasty one, of course. Who caused it? I think we all know the answer, but it can very easily be turned against the E.U.”

May’s short extension request left E.U. leaders facing a tricky decision: whether to grant the delay when they are unsure she can get the divorce deal approved by her own Parliament.

If the European Union were to offer a delay but the House of Commons then rejected the deal a third time, “then we are, I’m sorry to say, in God’s hands,” European Commission President Jean-Claude Juncker told Deutschlandfunk radio before May submitted her request. “But I think even God has a limit to his patience.”

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One major concern in Europe about a short extension is that if Britain did not take part in late-May elections for the European Parliament but then asked for yet more time at the end of June, the legal consequences could affect the basic functioning of European institutions.

Any E.U. citizen could potentially challenge laws passed by the new European Parliament, for example, because the bloc’s treaties require that all European citizens have the chance to vote and elect representatives to the body. Diplomats also worry that if British policymakers still have a say in E.U. decisions, they could hold unrelated deliberations hostage as a way to demand Brexit concessions.

The European Commission believes a June 30 Brexit delay poses serious risks, and Juncker “formally warned” May in a phone call Wednesday that she should not seek an extension later than the May 23 European elections if Britain does not plan to participate in them, Margaritis Schinas, a commission spokesman, said Wednesday. May ignored the warning.

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During Wednesday’s heated session in the House of Commons, Jeremy Corbyn, the leader of the opposition, said: “Today marks 1,000 days since the referendum, and this government has led the country and themselves into crisis, chaos and division.”

Later, Corbyn walked out of a meeting with May.

There was — again — renewed speculation over how long May can hold on to power. Lawmakers wondered what she meant when she said, “As prime minister, I am not prepared to delay Brexit any further than June 30.”