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.