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LONDON—Fresh from a difficult summit with other European Union leaders, Prime Minister Theresa May faces the defining weeks of her leadership, as she comes under growing pressure to seal a Brexit agreement and quell a rebellion in Parliament that threatens to force her from office.
But events are increasingly out of Mrs. May’s hands. The other 27 EU leaders reset the Brexit timetable on Thursday night with her out of the room.
Their new schedule is this: If she does beat the odds and secure approval for her EU divorce deal in the House of Commons next week, the U.K. will leave the bloc on May 22 and she will realize her oft-stated ambition of delivering Brexit. If her deal is defeated again, the new drop-dead date moves to April 12.
At that point, she will have to contemplate scenarios she has stubbornly resisted: a no-deal exit next month or a long Brexit delay to allow lawmakers to find an approach to Brexit they can agree on.
Patience with Mrs. May, who built her political career on unshowy pragmatism that now is seen as wooden and inflexible, is running out even among those who up to now have been loyal. Her inner circle of ministers is already jostling to position themselves should she quit, with several burnishing their euroskeptic credentials by voting last week against delaying Brexit.
Lawmakers complain of endless U-turns and a lack of clarity. If Mrs. May gives any further sign that Brexit will be again delayed past mid-April, “it is going to be very hard for her to continue,” said a member of the team responsible for enforcing party discipline in the House of Commons.
With the latest deal in Brussels, Mrs. May’s credibility has sunk further. She told Parliament on 108 occasions that the U.K. would leave on March 29, said Peter Bone, a euroskeptic Conservative lawmaker.
On Friday, anti-EU members of Parliament sought assurances that the Brexit uncertainty wouldn’t continue indefinitely.
If the U.K. is still in the EU after April, lawmakers want a pledge “the government would rather resign than be privy to such an appalling abuse of trust,” said Edward Leigh, a pro-Brexit Conservative lawmaker. Kwasi Kwarteng, a minister in the department for leaving the EU, called for “a degree of patience.”
“When you are in a hole, stop digging,” said Mark Francois, a Conservative lawmaker.
So far, she has been able to cling to her job, helped by the fact that after a failed putsch last year by her own Conservative lawmakers, according to party rules they can’t trigger a further no-confidence vote in her until December. Her party’s legislators don’t want to provoke a fresh election either, in case they lose ground to the main opposition Labour Party.
Nonetheless, the pressure on her to quit may become irresistible if her deal is killed off for good in the next three weeks.
Britain’s process of quitting the EU is still no clearer than it was six months ago. As EU leaders listened to Mrs. May explain her approach on Thursday, a number of them became even more pessimistic about its chances of success, according to several European officials.
That encouraged them to give British lawmakers extra breathing space to avoid an economically damaging no-deal exit, which until then loomed next Friday.
Unlike previous meetings with other leaders when Mrs. May read remarks and then left the room, this time she was peppered with questions, which she answered one by one. But she didn’t provide much illumination. “Her answers were rather flat, sticking to her script. She didn’t really explain anything,” said a European official briefed on the exchanges.
If her deal is again rejected, lawmakers will again be able to propose amendments to pave the way for alternative Brexit divorce plans, including possibly a referendum on whether to endorse Mrs. May’s deal or an alternative plan that keeps the U.K. in the EU’s single market.
But it isn’t clear if there is a majority for any form of Brexit in the House of Commons. Lawmakers are set to vote from Monday to determine the procedures to allow this to happen.
—Valentina Pop in Brussels contributed to this article.