WASHINGTON—Senate Republicans are considering whether to cut the corporate tax rate less deeply than President Donald Trump has demanded, a move that could make it easier to pass the tax bill they voted to begin debating Wednesday.

One of the most significant unresolved issues is whether the corporate tax rate should be set above the 20% threshold Mr. Trump has sought and how aggressively the administration would fight an attempt to set it higher. A final vote in the Senate could come as early as Thursday night.

Bumping...