Jordan said the differences between committee members might be so great that a deal becomes impossible. He noted members like Rep. Jeb Hensarling (R-Texas) and Sens. Pat Toomey (R-Pa.) and Rob PortmanRobert (Rob) Jones PortmanGOP defends Trump judicial nominee with no trial experience Bipartisan compromise is vital to the legislative process Senate GOP reveals different approach on tax reform MORE (R-Ohio) are "guys who understand you can't raise taxes."

On the other side, he said, are members like Sen. John KerryJohn Forbes KerryTrump's dangerous Guantánamo fixation will fuel fire for terrorists Tech beefs up lobbying amid Russia scrutiny Overnight Tech: Senate Dems want FCC chief recused from Sinclair merger | Tech rallies on Capitol Hill for DACA | Facebook beefs up lobbying ranks MORE (D-Mass.), whom he criticized for saying "ridiculous things" about House conservatives, such as blaming the Standard & Poor's downgrade on the Tea Party.

Jordan said it is not clear to him that the $1.2 trillion in automatic cuts would necessarily kick in if the supercommittee cannot reach an agreement.

"Well, I don't know that," he said when asked about the inevitability of the automatic cuts. "I hope we don't get there … Republicans, they don't want those defense cuts. We think that's the one are we're supposed to spend your tax dollars on."

Under the debt-ceiling deal, failure to find agreement on more cuts would trigger "sequestration" cuts to both defense and social service programs Democrats support. The deal was specifically designed this way to force both sides to reach an agreement.

Regardless how it turns out, Jordan said Republicans would continue to fight against any tax increases as part of the deal.

"But I guess I'm not overly optimistic that they are going to be able to reach an agreement that makes sense for the country, that actually reduces spending and doesn't raise taxes," he said.