WASHINGTON — With two days left before an 11-day recess and no vote scheduled, House Republican leaders considered last-minute changes to their latest bill to repeal the Affordable Care Act on Wednesday, including at least $8 billion in extra spending to answer the concerns of an influential Republican who had come out against the measure.

The scramble for votes — and a potential new willingness to throw money at the bill — underscored the price another failure would carry if Speaker Paul D. Ryan could not rally his considerable House majority around a legislative priority that Republicans have promised for seven years.

Republican leaders were ready to move on from health care after the embarrassing collapse of their measure in March, but President Trump pressed Mr. Ryan hard to deliver on a major campaign promise and personally pressured House members to fall into line.

If the effort fails, it will greatly weaken the president’s hand on Capitol Hill and cast a shadow across the rest of his legislative agenda, especially the deep tax cuts and rewrite of the tax code that he has proposed — and that are likely to be no easier to tackle than health care.