BRUSSELS — European Union leaders offered Theresa May sympathy but no promises Thursday as the British prime minister, weakened after a leadership challenge, sought a lifeline that could help her sell her Brexit divorce deal to a hostile U.K. Parliament.

May acknowledged that a breakthrough on her Brexit deal was unlikely even as she tried to get tweaks to it that she could use to win over opponents – particularly pro-Brexit lawmakers whose loathing of the deal triggered a challenge to her leadership this week.

EU leaders meeting in Brussels said they would try to be helpful, but would not reopen negotiations on a deal over Britain leaving the bloc that the two sides spent 18 months hammering out.

The outlook appeared bleak for May, who said she accepted that there was unlikely to be major progress on Brexit at the two-day EU summit. Underscoring the sense of stagnation, May’s office confirmed that the Brexit deal would not be put to a vote until 2019.

May said her focus “is on ensuring that I can get those assurances that we need to get this deal over the line.”

May caused an uproar in Parliament on Monday when she scrapped a planned vote on her Brexit deal to avoid certain defeat. That helped trigger a no-confidence vote among May’s own Conservative lawmakers on Wednesday. May won 200-117, but almost a third of her party’s lawmakers voted against her. And to secure victory, she promised she would step down as Conservative leader before Britain’s next national election, which is scheduled for 2022.

“In my heart, I would love to be able to lead the Conservative Party into the next general election,” May said Thursday. “But I think it is right that the party feels that it would prefer to go into that election with a new leader.”

She didn’t specify a date for her departure – and she did not say what she would do if her government lost a general no-confidence vote in Parliament called by the opposition and Britain faced an early national election. The opposition Labour Party feels emboldened by May’s troubles and is threatening to try and bring her government down.

The size of the rebellion within her own party underscores the unpopularity of May’s Brexit plan.

The 27 other EU nations are adamant there can be no substantive changes to the legally binding agreement on Britain’s withdrawal from the bloc but have suggested that there could be some “clarifications.” May was addressing those EU leaders before a summit dinner where they will discuss Brexit – and eat the meal – without her.

“The deal itself is non-negotiable,” Dutch Prime Minister Mark Rutte said. “So today is about clarification.”

French President Emmanuel Macron was equally firm.

“It is important to avoid any ambiguity,” he said. “We cannot reopen a legal agreement, we can’t renegotiate something which has been negotiated over several months.”

The Brexit deal has many critics but one intractable issue – a legal guarantee designed to prevent physical border controls from being imposed between Northern Ireland, which is part of the U.K., and the Republic of Ireland, a member of the EU. Northern Ireland’s 1998 peace accord depends on having an open, invisible border with Ireland.

A Brexit provision known as the backstop would keep the U.K. part of the EU customs union if the two sides couldn’t agree on another way to avoid a hard border.

Pro-Brexit lawmakers strongly oppose the backstop, because it keeps Britain bound to EU trade rules and unable to leave without the bloc’s consent. Pro-EU politicians consider it an unwieldy, inferior alternative to staying in the bloc.

Irish Prime Minister Leo Varadkar said he discussed possible remedies with May on Thursday.

“Some of the suggestions she made made sense, others I thought were difficult,” he said.

Varadkar said the EU might be able to give Britain “a greater assurance” that speedy talks on a new U.K.-EU trade deal would mean the backstop would never need to be used.

Among EU leaders there was admiration for what Rutte called May’s “tenacity and resilience” – but there was also exasperation at Britain’s domestic political mess.

“I don’t see that we can change this withdrawal agreement again,” German Chancellor Angela Merkel said. “We can, of course, talk about whether there should be additional assurances, but the 27 member states will be very united on this.”

Meanwhile, the clock is ticking down to Britain’s departure from the bloc, which is due to take place on March 29 – deal or no deal.

May’s office said Parliament’s vote on the Brexit deal, originally scheduled for this week, would be held “as soon as possible in January.”

Conservative lawmakers are still at loggerheads over the way ahead – for Brexit and for May. Dominic Raab, the U.K. Brexit secretary who quit last month in opposition to May’s deal, said he voted against her in Wednesday’s party ballot.

“(Now) we will have to back her as best we can,” he said, adding “(but) it looks very difficult to see how this prime minister can lead us forward.”

U.K. Foreign Minister Alistair Burt complained in a tweet that Conservative Brexiteers would never be satisfied.

“They never, ever stop. … After the apocalypse, all that will be left will be ants and Tory MPs complaining about Europe and their leader,” he wrote.

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