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 AlexanderMcCain urges 'a fresh start' on healthcare reform Schumer expresses hope for bipartisan ObamaCare fixes ObamaCare repeal: Now what? MORE (Tenn.), Richard BurrRichard BurrKushner says he did not collude with Russia, had no improper contacts Dems slam Trump for 'stonewalling' oversight efforts Burr: Nunes 'created' unmasking allegations against Rice MORE (N.C.), Saxby ChamblissSaxby ChamblissFormer GOP senator: Let Dems engage on healthcare bill OPINION: Left-wing politics will be the demise of the Democratic Party GOP hopefuls crowd Georgia special race MORE (Ga.), James InhofeJames InhofeMcCain absence adds to GOP agenda’s uncertainty GOP signals infrastructure bill must wait Lobbying World MORE (Okla.), Johnny IsaksonJohnny IsaksonOvernight Finance: House votes to repeal arbitration rule | Yellen, Cohn on Trump's list for Fed chief | House passes Russia sanctions deal | GOP centrists push back on border wall funding Senators urge quotas on Canadian lumber, consultations with Congress Trump labor board nominees advance in Senate MORE (Ga.), Mark KirkMark KirkMcConnell: Senate to try to repeal ObamaCare next week GOP senator: Not 'appropriate' to repeal ObamaCare without replacement GOP's repeal-only plan quickly collapses in Senate MORE (Ill.) and John McCainJohn McCainDon’t let Congress throw away our right to health 19 attorneys general urge Congress to block Trump's transgender troop ban McCain urges 'a fresh start' on healthcare reform MORE (Ariz.).

Freshman Sen. Joe ManchinJoe ManchinSenate heading for late night ahead of ObamaCare repeal showdown Overnight Healthcare: Four GOP senators threaten to block 'skinny' repeal | Healthcare groups blast skinny repeal | GOP single-payer amendment fails in Senate GOP single-payer amendment fails in Senate MORE (D-W.Va.) on Tuesday announced his support for the "CAP Act."