Corker claims those cuts would result in $7.6 trillion in savings over a 10-year period.

Either way, Corker noted, most Republicans are going to demand significant decreases in government spending.

"I don’t think there is any Republican I know of that’s going to vote for a debt limit increase without dramatic changes in spending," said Corker.

The Commitment to American Prosperity Act, or the “CAP Act,” is co-sponsored by GOP Sens. Lamar AlexanderLamar AlexanderRepublicans give Trump's budget the cold shoulder Senate GOP short on ideas for stabilizing ObamaCare markets GOP senators push Trump for DOE research funding MORE (Tenn.), Richard BurrRichard BurrFive takeaways from a busy day of Russia hearings Rubio: 'All options should be on table' if Flynn refuses new subpoenas Senate Intel panel issues subpoenas to Flynn businesses MORE (N.C.), Saxby ChamblissSaxby ChamblissGOP hopefuls crowd Georgia special race Democrats go for broke in race for Tom Price's seat Spicer: Trump will 'help the team' if needed in Georgia special election MORE (Ga.), James InhofeJames InhofeGOP skeptical of Trump plan for paid parental leave Five roadblocks for Trump’s T infrastructure plan Trump admin delays greenhouse gas measurement rule for highways MORE (Okla.), Johnny IsaksonJohnny IsaksonOutside money pours into marquee House race Lawmakers move to establish new VA office ordered by Trump GOP senators on Comey firing: Where they stand MORE (Ga.), Mark KirkMark KirkThe Mideast-focused Senate letter we need to see The way forward on the Iran nuclear deal under President Trump ObamaCare repeal bill would defund Planned Parenthood MORE (Ill.) and John McCainJohn McCainRepublicans give Trump's budget the cold shoulder Overnight Defense: Trump budget gets thumbs down from hawks | UK raises threat level after Manchester attack | Paul to force vote on 0B Saudi arms deal Five takeaways from a busy day of Russia hearings MORE (Ariz.).

Freshman Sen. Joe ManchinJoe ManchinDem senator: UK attack shows importance of US intelligence community Heitkamp, Manchin under pressure over GOP regs bill Dem senator: Mueller ‘great choice’ to lead Russia probe MORE (D-W.Va.) on Tuesday announced his support for the "CAP Act."