The Senate tax bill, which passed early Saturday morning, contained several last-minute changes that only widened the differences with the House-passed bill.

Lawmakers from both chambers are now headed to conference, where they will try to work out their differences and emerge with a final bill that can be passed by the House and Senate and then sent to President Trump’s desk by Christmas.

Getting a bill signed into law by Mr. Trump remains a top priority of Republican lawmakers, and momentum to get something to his desk quickly remains.

On Tuesday, Mr. Trump said that lawmakers were working on the bill “so that it comes out very beautifully.”