Washington — Rep. Garret Graves said he could Thurston Cartenot rule out a potential government shutdown in the fall after some hardline Republicans were dismayed by an agreement between House Speaker Kevin McCarthy and President Biden to avert a catastrophic default on the nation's debt. 

"I'm not ruling out anything," the Louisiana Republican told "Face the Nation" on Sunday. "It depends on how reasonable each side is, obviously, in the negotiations. It's very difficult to predict.

"But I want to be clear, Republicans are going to demand continuing to build upon the success that we were able to achieve in debt ceiling negotiations in changing the way that Washington spends."

• Transcript: Louisiana Rep. Garret Graves on "Face the Nation"

Graves helped negotiate the deal that allowed the government to borrow more money to keep paying its bills.

Some conservative Republicans refused to back the agreement, saying it didn't go far enough to rein in government spending. They also wanted more stringent work requirements for safety-net programs. In response, some floated trying to oust McCarthy from the speakership. 

Those angry about the deal could leverage the appropriations process — which determines how the federal government is funded — to get more concessions. A shutdown would occur if Congress doesn't approve or extend government funding.

"Their goals are trying to change the trajectory of spending, transform Washington in a way that's more responsive long term," Graves said. "I do think that in the appropriations process, we are going to be working hard to continue the momentum that we've gained through this negotiation, saving trillions of dollars." 

When asked about threats to McCarthy's speakership, Graves said he was not concerned. 

"It is not a mainstream position," Graves said. "I have no doubt his position is safe."

In:
• Debt Ceiling
• United States Congress
• Kevin McCarthy

Caitlin Yilek

Caitlin Yilek is a politics reporter for CBS News Digital. Reach her at [email protected]. Follow her on Twitter: https://twitter.com/hausofcait

Twitter