"We're working on that right now. ... We do need to have this trigger worked out before the budget vote today," Corker told Fox News, when asked if he thought the tax bill would be able to pass the Budget Committee and ultimately the entire Senate.

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"I know it's important, not just to me but numbers of members who want to make sure that if for some reason these projections are off, we don't have the growth that's been laid out ... that we're not passing on increased debt to future generations," Corker told CNBC.

Pressed if under the "trigger" taxes on individuals would go up, Corker added: "And businesses ... We're working through that right now. ... You know, just let it play out."

President Trump is expected to discuss tax reform with Senate Republicans during their weekly caucus lunch on Tuesday.

Corker, arguing he hadn't made demands on the tax plan, said he was willing to "swallow" the provisions in the legislation reforming the individual tax code in exchange for getting more help for cooperations.

"If we could take the entire individual side of this, throw it in the trash can and take it directly to the incinerator — I would be thrilled if we were only dealing with the business side," he said.

GOP leadership is hoping that lawmakers will reserve their "no" votes for the Senate floor, allowing the bill to move forward on Tuesday.

But they have an equally narrow path once the bill reaches the floor. With a 52-seat majority, they can only afford to lose two GOP senators and still have Vice President Pence break a tie.

McConnell started the process on Monday night of placing the House-passed tax plan on the Senate calendar. The move, once completed, would allow GOP leadership to use the bill as a vehicle for any Senate tax legislation.