Lawmakers are at an impasse on how to pass a continuing resolution (CR) to fund the government, which has been shut down for a week. They are also working against an Oct. 17 deadline for raising the nation's borrowing limit. 

Treasury and the White House have warned that if the limit is not lifted, the government could default on its debt, leading to a recession. 

Coburn said Congress shouldn’t increase the debt ceiling because it would “let the politicians off the hook” of making tough decisions on spending reductions.

“I think we ought to be about cutting up the credit card,” Coburn said. “I don’t believe we ought to have another debt limit increase. … We need to be forced to make the hard choices.”

House Republicans have demanded that repealing parts of ObamaCare be included in a debt ceiling increase and Senate Republicans have called for major entitlement reform to reduce spending. President Obama has demanded that Congress sent him a "clean" debt ceiling increase.

It's unclear where the fight will go from here as each side becomes more entrenched.