The Senate Budget Committee voted 12-11 to advance the bill as two committee Republicans who had said they were considering voting against the measure - Bob Corker of Tennessee and Ron Johnson of Wisconsin - backed the legislation.
The Republican president told reporters Tuesday that they were in a "very good position" after the Senate Budget Committee's passage of the GOP tax plan. Lawmakers must renew government funding before it expires on December 8.
A new ad set to air on television Tuesday paints the bill as a win for the rich, including President Donald Trump.
Democrats are already running ads against Republicans for the plan.
Senator Cory Gardner, a Colorado Republican, said he plans an amendment to make marijuana businesses eligible for tax breaks. "Think of sitting there with a Rubik's cube".
"I am not going to vote to automatically implement tax increases on the American people", said Sen.
"Let it sit out there in the sun. and let it bake", he said, demanding more time for Americans to understand the implications of the proposal.
The House's chief tax-writer says ending the "Obamacare" requirement that everyone have health insurance - an element of the Senate bill - is a move the House also is likely to accept.
The Senate bill would keep seven individual tax brackets, similar to current law, while the House bill would have four brackets.
Amid the drama of a quintessential Washington cliffhanger Tuesday, it was unclear whether the uncertainty was typical of habitual deal-making and brinkmanship over the fate of a major bill, or whether tax reform measure, a hugely significant political lift for Republicans was actually in trouble. Lawmakers "alarmed" by EPA's science board changes MORE (Pa.), Patrick Meehan (Pa.), Dave ReichertDavid (Dave) George ReichertMounting GOP retirements threaten House majority The Hill's Whip List: Where Republicans stand on tax-reform bill The future lies in the Asia-Pacific MORE (Wash.) and Michael Turner (Ohio). "With just a few changes, some mathematical, the middle class and job producers can get even more in actual dollars and savings". Trump said in his latest tweet on the tax bill.