The House of Representatives earlier approved the bill comfortably. Republicans have majorities in both houses of Congress.
For final approval the legislation must go back to the House on Wednesday for a procedural issue.
If it passes, as expected, it will be President Donald Trump's first major legislative triumph.
Critics say the package is a deficit-bloating giveaway to the super-rich.
But Republicans argue the tax cuts for corporations, small businesses and individuals will boost economic growth.