“What is the alternative action available to us?” Mr. Johnson told lawmakers as he rallied them round the deal. “To undo Brexit?”

Mr. Johnson said he would pull his Brexit deal altogether if Parliament attempted to block its progress and delayed ratification until January.

A victory in the vote wouldn’t on its own bring to an end the protracted deadlock on how and when the U.K. should break from the EU: Lawmakers will vote later Tuesday whether to accept his government’s preferred timetable of just three days to make the legislation law, and will likely balk at waving the deal through so quickly. That will give Mr. Johnson’s opponents further opportunities to try to amend or frustrate the deal.

Mr. Johnson’s government argues that after three years of political wrangling, Brexit needs to be concluded. He wants Parliament to approve it at record speed, with lawmakers wrapping up deliberations on the bill by Thursday and the House of Lords working over the weekend to get it over the line. Britain’s departure from the EU has been delayed twice since 2016’s referendum and Mr. Johnson is loath to delay once more.

“I will in no way allow months more of this,” he said.

Government officials are confident they have the votes in the House of Commons to pass the deal, though margins are slim. If they fail, the Brexit impasse would likely have to be resolved through a general election.

Even if the deal passes, lawmakers could vote to slow down scrutiny of the law, jeopardizing Mr. Johnson’s pledge to get the U.K. out of the EU by the current deadline of Oct. 31. Any delay beyond that date would need to be agreed by the 27 other EU governments—though their agreement is highly likely.

If lawmakers do approve the accelerated timetable, they could hold further votes to try to change the legislation.

Lawmakers have already begun publishing proposed amendments to the agreement. Former Conservative legislator Kenneth Clarke, now an independent lawmaker, wants the U.K. to be more closely bound to the EU, remaining in a customs union with the bloc after Brexit.

Other amendments expected to be voted on include one to subject the deal to a public referendum, offering the option of staying in the EU. It is unclear whether either of these proposals will garner a majority, but they will need time to be debated.

Given that this summer British lawmakers spent nearly a month debating a law to ban the use of wild animals in traveling circuses, passing a law that will define Britain’s split with its biggest trade partner in just a few days is a tall order, analysts say.

Furthermore, some details are scant: The U.K. Treasury hasn’t published an assessment of economic impact it would have on the U.K., for instance.

Previous EU related laws have taken a long time to pass. The EU Withdrawal Act, which paved the way for the U.K. leave the bloc, took up 273 hours of parliamentary time. The Maastricht treaty, which accelerated the integration of the European bloc in the early 1990s, was debated for 21 days in Parliament.

If the government’s proposed schedule is voted down, it could propose another timetable after consulting with lawmakers. Or it could simply try to curtail the ongoing debate when the deadline approaches by tabling a special motion, which again would be subject to voting.

Another issue is what happens after Brexit.

Currently Britain is due to enter a transition period with the EU up until the end of 2020—with possible further extensions until the end of 2022—while the two sides negotiate a trade deal.

Some lawmakers fear the U.K. won’t have negotiated a comprehensive trade deal with the EU by the end of next year and fear a cliff edge in which Britain’s ties with its biggest trading partner will be severely curtailed. They want a guarantee the U.K. will ask to extend the transition period until 2022, a step pro-Brexit lawmakers oppose.

Write to Max Colchester at max.colchester@wsj.com