The House on Tuesday narrowly passed a Republican budget resolution that calls for $4.5 trillion in tax cuts and a $2 trillion reduction in federal spending over a decade, clearing the way for major elements of President Trump’s domestic agenda.

The nearly party-line vote of 217 to 215 teed up a bitter fight within the G.O.P. over which federal programs to slash to partially finance a huge tax cut that would provide its biggest benefits to rich Americans.

It came after a head-spinning hour in which Republican leaders tried to put down a revolt among conservatives who wanted deeper spending cuts, failed to do so, canceled the budget vote and then reversed course minutes later and summoned lawmakers to call the roll.

The chaotic scene underscored the unwieldy path House Republicans have ahead of them as they try to push through Mr. Trump’s domestic policy agenda through Congress over the objections of Democrats.

Approval of the budget plan was a crucial first step for Republicans to smooth the way through Congress for an enormous fiscal package using a process called reconciliation, which allows such bills to steer clear of a filibuster and pass the Senate on a simple-majority vote.