On the eve of a critical parliamentary vote, Britain’s prime minister, Theresa May, flew to Strasbourg, France, on Monday in the hope of rescuing her unpopular plan for exiting the European Union from a second, potentially terminal, defeat.
Even for Mrs. May, who has made a habit of pushing decisions to the wire, Monday night’s mission came at the 11th hour. It ended a day of political confusion, swirling speculation and high-wire negotiation with her European counterparts.
But there was no immediate reason to think that the concessions on offer from the European Union 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.
On Monday, after a telephone call with Jean-Claude Juncker, president of the European Commission, Mrs. May set up a meeting with him in Strasbourg, where the European Parliament is holding a plenary session.
Tuesday’s vote is seen as a pivotal moment in the endless withdrawal saga, known as Brexit, coming less than three weeks before the deadline for Britain to leave the European Union.
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, Mrs. May’s Brexit withdrawal proposals were defeated by 230 votes in the 650-seat Parliament, one of the greatest defeats in British history.
Since then she has sought unsuccessfully for assurances that a “backstop” provision to prevent a hard Irish border would have a clear end point, as pro-Brexit lawmakers have demanded.
That is a formidable task. But if Mrs. May can at least limit the size 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.
Critical to the success of the talks has been the figure 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 would have to judge them helpful in averting the risk that Britain might be trapped indefinitely in the backstop. But Mr. Cox took part in discussions in Brussels last week without much success.
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 ConservativeHome 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.”