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 AlexanderAndrew (Lamar) Lamar AlexanderObamaCare becomes political weapon for Democrats Senate passes resolution requiring mandatory sexual harassment training Sen. Warren sold out the DNC MORE (Tenn.), Richard BurrRichard Mauze BurrJuan Williams: The shame of Trump's enablers Five takeaways from the social media hearings Overnight Tech: Senators demand tech firms do more on Russian meddling | House Intel releases Russian-promoted ads | Apple CEO says 'fake news' bigger threat than ads | Ex-Yahoo CEO, Equifax execs to testify on breaches MORE (N.C.), Saxby ChamblissSaxby ChamblissLobbying World Former GOP senator: Let Dems engage on healthcare bill OPINION: Left-wing politics will be the demise of the Democratic Party MORE (Ga.), James InhofeJames (Jim) Mountain InhofeMcCain backs Pentagon nominee despite concerns over defense industry ties GOP senators ask Trump for meeting on biofuels mandate Trump feuds endangering tax reform MORE (Okla.), Johnny IsaksonJohn (Johnny) Hardy IsaksonCongress is working to honor America’s heroes Bipartisan lawmakers can rebuild trust by passing infusion therapy bill 24 senators co-sponsor bipartisan ObamaCare deal MORE (Ga.), Mark KirkMark KirkHigh stakes as Trump heads to Hill Five things to watch for at Trump-Senate GOP meeting Giffords, Scalise highlight party differences on guns MORE (Ill.) and John McCainJohn Sidney McCainGOP rushes to cut ties to Moore GOP strategist: 'There needs to be a repudiation' of Roy Moore by Republicans World leaders reach agreement on trade deal without United States: report MORE (Ariz.).

Freshman Sen. Joe ManchinJoseph (Joe) ManchinDems mull big changes after Brazile bombshell A bipartisan bridge opens between the House and Senate Collins, Manchin to serve as No Labels co-chairs MORE (D-W.Va.) on Tuesday announced his support for the "CAP Act."