But Republicans will not stop the measure on Tuesday. More than 220 Democrats and one Republican — Representative Justin Amash of Michigan — have signed on to the resolution of disapproval, which Congress can use to end the emergency status under the National Emergencies Act if the threat has dissolved or if there is concern that the president has used his powers irresponsibly. That is already more than enough to clear the House.

Ms. Pelosi noted that extending an offer to Republicans to join Democrats in sponsoring the resolution was a courtesy.

“What’s really important is how they will vote when it comes to the floor,” she said. “We’ll see where they come down on that.”

Representative Joaquin Castro, Democrat of Texas and the author of the resolution, said that he planned to spend the weekend calling his colleagues and rallying support for the measure. He said he and his staff had been working on the one-page measure for weeks in anticipation of a declaration.

“This is an historic power grab and it will require historic unity by members of Congress,” he said on Friday, calling the declaration a “parasitic movement” from the president.

“If the Congress rolls over on this, the president is likely to do it again,” he added.

By law, the Senate will have to take up the measure within 18 days of its passage in the House, where a floor vote is expected within 18 days after a committee vote. Senator Mitch McConnell of Kentucky, the majority leader, has in the past been a fierce defender of Senate prerogative, but he backed Mr. Trump’s declaration this month to secure passage of a major spending bill that funds the government through the fiscal year.

Senator Chuck Schumer of New York, the Democratic leader, said in a statement on Thursday that identical companion legislation would soon be introduced in the Senate. The Senate could also move to amend the resolution that is expected to pass through the House.