Some Republican senators haven't yet committed to supporting the GOP tax bill, but anti-tax crusader Grover Norquist said he thinks, in the end, the party will pass the legislation.
Republicans, who hold 52 Senate seats, can only lose two votes and still pass the bill under special budget rules, assuming all Democrats and independents vote against it.
Norquist said two Republicans can take a stand and vote against it and no one will remember their names.
However, if three people do it, they become famous, he said in an interview with "Power Lunch" on Tuesday.
"It goes into their obituaries that their last political act was to sink a tax cut that would help 25 million small businesses and reduce taxes across the board because they were in a pissing match over tweets. It would make them look small," he said.
The Senate Budget Committee advanced the bill to the floor on Tuesday afternoon.
Earlier Tuesday, Sen. Bob Corker, R-Tenn., told CNBC a "backstop" to curb future budget deficits could help win his vote. He also said it is "ridiculous" that anyone could claim he would vote against something "that's good policy because of some rift that's occurring."
Corker backed the proposal after reportedly reaching the outline of a deal for such a backstop.
All three have spoken out against President Donald Trump.
"None of those three gentlemen are small. They are grownups; they are serious senators. They are not going to make themselves look small by voting against a bill that they know ... is a strong, pro-growth, helpful bill," said Norquist.
Sen. Ron Johnson of Wisconsin has also been one of the GOP holdouts, expressing concerns about the "pass-through" treatment of business income. He also ended up voting to advance the bill.
— CNBC's Jacob Pramuk contributed to this report.