House Minority Leader Kevin McCarthy, R, said that he wasn't sure how many Republicans would vote for the resolution, "but there will not be enough to override any veto."
The outcome was less assured in the Senate, which will be required - under provisions of the National Emergencies Act - to take up the legislation within weeks of House passage. If all Senate Democrats vote for the disapproval resolution, only four Republican votes would be needed to ensure passage, since just a simple majority vote is required.
With numerous Republican senators voicing concerns or outright opposition to Trump's national emergency declaration, the disapproval resolution was widely expected to pass the Senate - though probably without securing the two-thirds majority that would be needed for a veto override.
Senators could also potentially vote to amend the resolution, which could complicate its path to passage.
Trump urged GOP senators to stick with him, writing on Twitter: "I hope our great Republican Senators don't get led down the path of weak and ineffective Border Security. Without strong Borders, we don't have a Country - and the voters are on board with us. Be strong and smart, don't fall into the Democrats "trap" of Open Borders and Crime!"
Democrats contended that Trump was declaring an emergency where none existed, and they argued that he was usurping Congress' constitutional authority over government spending. They said the real issue at stake is not Trump's border wall, but the Constitution and its separation of powers.
"It was a lawless act, a gross abuse of power, and an attempt by the president to distract from the fact that he broke his core promise that Mexico pay for the wall," Senate Minority Leader Chuck Schumer said. "There's no evidence of an emergency at the border."