WASHINGTON—President Donald Trump will meet with Senate Republicans at their weekly closed-doors lunch on Tuesday, a top GOP lawmaker said Friday, as the party prepares to vote next week on legislation overhauling the tax code.

The Senate Budget Committee is expected to merge key pieces of the legislation on Tuesday, ahead of a full chamber vote later that week, according to a Senate GOP aide. That timetable could shift if GOP leaders come up short on the votes needed to pass it.

Republicans hold a 52-48 majority in the Senate and can afford to lose no more than two GOP votes on the tax bill, provided that no Democrats support it. Vice President Mike Pence would cast any tiebreaking vote.

House Republicans passed their version of the tax bill shortly before the Thanksgiving break. But passage in the Senate is expected to be more of a nail-biter, with many Republicans undecided on the bill.

Mr. Trump is expected to discuss the tax bill and the rest of the year-end legislative agenda at the Tuesday lunch, the office of Senate GOP Policy Committee Chairman John Barrasso said Friday.