Trump said last week that he would veto the measure "100 percent" if that happened. And he predicted that Congress would be unable to muster the votes to override his veto.
As the House vote approaches, Trump is facing a fresh backlash from fellow Republicans.
A group of 25 former Republican members of Congress has written an open letter urging a termination of the emergency declaration.
The letter argues that Trump is encroaching on Congress's "power of the purse" and urges current lawmakers to stand up for its constitutional powers.
"We who have served where you serve now call on you to honour your oath of office and to protect the Constitution and the responsibilities it vested in Congress," says the letter.
Its signers include former senators John Danforth of Missouri, Chuck Hagel of Nebraska, Gordon Humphrey of New Hampshire, Richard Lugar of Indiana, Olympia Snowe of Maine, and 18 former House members.
A bipartisan group of 58 former senior national security officials also plans to issue a statement saying that "there is no factual basis" for Trump's proclamation.
The former officials' statement, which will be entered into the Congressional Record, is intended to support lawsuits and other actions challenging the national emergency proclamation and to force the Administration to set forth the legal and factual basis for it.