"And I say that because I believe that he believes that it endures to his political benefit," he added. "We have no desire for the government to close, none whatsoever. We do desire that the processes of government work."

Republicans are split over whether to use the upcoming fight over the debt limit and 2014 spending levels to defund ObamaCare. Dozens of House Republicans called on House leaders to pursue that strategy next month, which some say could lead to a government shutdown.

House leaders, however, seem to be resisting that strategy.

The upcoming battle is reminiscent of 2011, which led Congress to pass the Budget Control Act. That law led to the sequester, and two years later, the two parties are still largely frozen when it comes to sorting out a big compromise on taxes and spending.

Price indicated that the splits on Capitol Hill are similar to those among Americans in general.

"Your Congress for better or worse is a pretty darn good representation of the nation," he said.