Mark Meadows and House Minority Leader Kevin McCarthy urged their colleagues to vote against the resolution, while Democratic Rep.
Jamie Raskin and House Speaker Nancy Pelosi said lawmakers should pass it and 'move toward peace, not escalation of hostilities'.
The vote in the Democratic-controlled House was due Thursday afternoon.
Passage would send it to the Senate, where its fate was uncertain.
Trump's fellow Republicans hold 53 seats in the 100-member Senate, but at least two members of his party - Senators Rand Paul and Mike Lee - have expressed support for the resolution.
Trump told reporters at the White House he did not think he had to seek congressional approval for military action against Iran.
The War Powers Act was passed in 1973, as lawmakers reacted to secret bombings during the bitterly divisive Vietnam War.