WASHINGTON—Senate Republicans trudged through a marathon session that stretched from Monday morning into early Tuesday, struggling to corral enough votes to pass the party’s “big, beautiful bill” and move the legislation one step further toward President Trump’s desk ahead of lawmakers’ self-imposed July 4 deadline.

Voting on amendments and procedural motions started midmorning Monday and dragged through the night into the next morning as Republican leaders worked to find a balance of policies that could pass both the Senate and later the House. Trump spoke with congressional leaders by phone, and the White House said it was confident that the bill was on track even as its fate and final content remained uncertain.