The budget plan that Republicans squeezed through the House on Tuesday night was the first step in unlocking President Trump’s legislative agenda.

But despite the drama surrounding the close vote, that was the easy part. Now Republican leaders must begin the process of determining which of Mr. Trump’s priorities can make it into an enormous bill they must try to pass through Congress.

It will be an extraordinarily difficult and politically tricky balancing act that will require weighing the president’s demands for a slew of expensive proposals — such as eliminating tax on tips and permanently extending the 2017 tax cuts — against his promises to protect programs like Medicare and Medicaid from cuts.

While Mr. Trump has never been particularly concerned about debt or deficits, a number of the Republicans whose votes G.O.P. leaders need to push the legislation through Congress are. And they have signaled that they will be unwilling to lend their support to any measure that balloons the debt.

What happens next?

House Republicans will turn to writing the legislation that will lay out the policy changes they want in order to reach the spending targets laid out in their blueprint. Before the House votes on that legislation, the Senate will also have to pass its own blueprint. The resulting product would be shielded from a Senate filibuster, allowing Republicans to steer around Democratic opposition and pass it on a simple majority vote.

But achieving unity between the two chambers could be an issue. Republican leaders in the House and the Senate are divided over how best to advance Mr. Trump’s agenda. House Republicans want to pass what the president has called “one big, beautiful bill,” including huge tax cuts and investments in immigration enforcement as well as spending reductions. Senate G.O.P. leaders want to move quickly to pass legislation increasing funding for the military and border security efforts, then follow up with another expansive bill that would make the 2017 tax cuts permanent.