BRUSSELS (AP) - In a week of damaging political blows over her handling of both Brexit and her job, British Prime Minister Theresa May insisted Thursday she can still get her European Union divorce agreement approved in Parliament - with a little help from her EU friends.

May implored the 27 other EU leaders at a Brussels summit to help her sell the Brexit deal to hostile British lawmakers by adding “extra assurances” about the vexed issue of the Irish border.

“There is a majority in my Parliament who want to leave with a deal, so with the right assurances this deal can be passed,” May said, warning her EU counterparts that failure could mean Britain crashing out of the bloc without a deal, “with all the disruption that would bring.”

EU leaders responded with sympathy but insisted they would not reopen negotiations on a divorce deal that the two sides spent a year and a half hammering out.

May acknowledged a breakthrough on her Brexit deal was unlikely at the two-day summit, 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.

“I don’t expect an immediate breakthrough, but what I do hope is that we can start work as quickly as possible on the assurances that are necessary,” May said.

May’s week from hell began Monday, when she scrapped a planned vote in Parliament on her Brexit divorce deal at the last minute to avoid a heavy defeat.

Anger at the move helped trigger a no-confidence vote among May’s own Conservative lawmakers on Wednesday. May won 200-117, but more than 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.”

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

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.

May told EU leaders that to win U.K. backing for the deal, “we have to change the perception that the backstop could be a trap from which the U.K. could not escape.”

But while Britain would like a guarantee that the backstop will be temporary, the EU insists there can be no fixed end date.

“If the backstop has an expiry date, if there is a unilateral exit clause, then it is not a backstop,” said Irish Prime Minister Leo Varadkar. “That would be to render it inoperable.”

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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Associated Press writers Danica Kirka in London, Geir Moulson in Berlin and Lorne Cook in Brussels contributed to this report.

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This story has been corrected to show that 117 Conservative lawmakers is just over a third of the total not just under a third.

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Follow AP’s full coverage of Brexit at: https://www.apnews.com/Brexit

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