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.
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Freshman Sen. Joe ManchinJoe ManchinOvernight Finance: Trump threatens NAFTA withdrawal | Senate poised for crucial Puerto Rico vote | Ryan calls for UK trade deal | Senate Dems block Zika funding deal Overnight Energy: Volkswagen reaches .7B settlement over emissions Senators rally for coal miner pension fix MORE (D-W.Va.) on Tuesday announced his support for the "CAP Act."