The vote to open a war powers debate, a pair of attempted veto overrides and a split on health care suggested a greater appetite among Republicans to challenge the president.
House votes to override a pair of Trump vetoes were an unusual bid by some in the G.O.P. to assert their own branch’s prerogatives. But they fell short.
A handful of Republicans joined Democrats to allow the measure to move forward, reflecting concerns in both parties about the administration’s strategy.
“Make no mistake: Bombing another nation’s capital and removing their president is an act of war, plain and simple,” Senator Rand Paul, Republican of Kentucky, said before the vote.
The Republican defectors paved the way for a debate that could expose bipartisan concern about President Trump’s actions in Venezuela. Mr. Trump called for them to lose their seats.