LONDON — On the eve of a critical parliamentary vote, Britain’s prime minister, Theresa May, secured new legal pledges from the European Union in a last-minute effort to rescue her unpopular plan for exiting the European Union from a second, potentially terminal, defeat.
But it was unclear that the concessions agreed by the European Union negotiators would be enough to prevent another defeat of Mrs. May’s deal in Parliament on Tuesday — one that could threaten her control over the process, or even her job. The initial reaction of pro-Brexit hard-line lawmakers ranged from critical to cautiously positive.
Even for Mrs. May, who has made a habit of pushing decisions to the wire, Monday night’s agreement, struck in Strasbourg, France, came at the 11th hour.
It ended a day of political confusion, swirling speculation and high-wire negotiation with her European counterparts.
On Monday, after a telephone call with Jean-Claude Juncker, president of the European Commission, Mrs. May flew to meet him in Strasbourg, where the European Parliament is holding a plenary session.
Back in London, David Lidington, Mrs. May’s de facto deputy, told Parliament that the prime minister had won a legal pledge to reassure pro-Brexit lawmakers who fear that Britain could be trapped indefinitely inside parts of the European Union’s economic rule book.
The new provisions in a “joint instrument” clarify the temporary nature of the so-called Irish “backstop” provision, which is part of the withdrawal agreement. This provision is designed to prevent a hard border being created between Ireland, which will remain in the European Union, and Northern Ireland, which is part of the United Kingdom.
Tuesday’s vote is seen as a pivotal moment in the endless withdrawal ordeal, known as Brexit, coming less than three weeks before the deadline for Britain to leave the European Union.
Speaking late on Monday, Mr. Lidington appealed to lawmakers to support Mrs. May’s deal, telling them the alternative was to “plunge this country into a political crisis.”
If there is no agreement by March 29, Britain will depart the bloc without any deal. That could mean a brutal economic adjustment, as the terms of trade would change overnight, disrupting the flow of goods to and from the continent.
In January, the prime minister’s Brexit withdrawal proposals were defeated by 230 votes in the 650-seat Parliament, one of the greatest defeats in British history.
Overturning that is a formidable task. But if Mrs. May can at least limit the size of a second defeat, she might be able to kick the can down the road one last time.
Under that scenario she might seek one further concession at a summit of European Union leaders on March 21, then perhaps hold a third — final — vote on her deal just before Britain’s scheduled departure, offering it as the only alternative to delaying Brexit.
Lawmakers, however, are getting restive and are threatening to try to seize control of the process.
Mrs. May has promised that if Parliament rejects her deal again on Tuesday, it will be offered votes on whether to leave the bloc without an agreement, something that a majority of lawmakers oppose. If they decide against that, legislators would then be allowed another vote on whether Britain should request an extension of its negotiations with Brussels.
Mrs. May is increasingly trapped between warring factions of her own Conservative Party.
One group is determined to prevent the prospect of a potentially chaotic “no deal” departure. But another faction wants to keep that option open in the hope that the threat of a disorderly Brexit would force a better deal out of European nations, whose economies would also suffer.
On Monday rumors surfaced that, facing certain defeat, Mrs. May might use a parliamentary mechanism to wriggle out of the vote that she promised lawmakers for Tuesday. But she retreated when that provoked a backlash from some legislators. The focus then switched back to the last-minute negotiations with the European Union.
For days there had been deadlock over the Irish border issue, and the hard-line Brexiteers demand for an exit clause, or a time limit.
Neither of those two demands appeared to have been met by Monday night’s changes, which essentially gave more legal force to existing pledges that the backstop would be temporary.
Mrs. May said in a statement that, in addition to the pledge in the “joint instrument,” there would also be a statement from both sides promising to begin work immediately to replace the backstop with alternative arrangements.
And Britain would make its own unilateral declaration stating that, if the backstop were invoked, but seemed to be becoming permanent and efforts to resolve the situation reached an impasse, London would seek to extract itself from it.
“Today we have secured legal changes,” Mrs. May said, “now is the time to come together, to back this improved Brexit deal, and to deliver on the instruction of the British people.”
Mr. Juncker said the backstop was “an insurance policy, nothing more, nothing less.”
“The intention is for it not to be used, like in every insurance policy,” he added.
Whether all this satisfies critics will depend in part on the judgment of Geoffrey Cox, the attorney general, whose booming voice, theatrical style and ideological support for Brexit have won him plaudits within Conservative ranks.
For concessions from the European Union to have an impact on pro-Brexit lawmakers, Mr. Cox will have to persuade them that they avert the risk that Britain might be trapped indefinitely in the backstop.
A critical test will be whether he persuades 10 lawmakers from Northern Ireland’s Democratic Unionist Party who normally prop up the government but have opposed Mrs. May’s Brexit plan.
If the D.U.P. can be brought on board that could persuade a number of Conservative pro-Brexit lawmakers to follow suit.
Jeremy Corbyn, leader of the opposition Labour Party, said Mrs. May’s negotiations had failed. “This evening’s agreement with the European Commission does not contain anything approaching the changes Theresa May promised,” he said in a statement.
Mrs. May’s strategy has been to try to whittle down opposition to her deal in Parliament, warning more pro-European critics that Britain could leave without any agreement, while telling Brexit supporters that a delay to withdrawal could mean that it never happens.
But the threats seem to have had a diminishing impact. Pro-Europe lawmakers believe they have the numbers in Parliament to stop a no-deal departure.
Last week one pro-Brexit legal expert, Martin Howe, argued there was nothing to fear even from a long extension of talks.
In an article on the Conservative Home website, Mr. Howe argued that Britain would be “much better off than under the deal” negotiated by Mrs. May, and would be “free to leave on 1 January 2021 without being trapped in the ‘backstop’ protocol.”