Because both outcomes are equally bad, Garrett said he is one of many members who will insist on spending limits as part of the debt-ceiling vote, which he said is expected to come sometime between late May and August. He added that this demand means it is not a sure thing that an agreement can easily be worked out.

"It's certainly a long thing from a done deal," he said. "There are a lot of members in Congress, myself included, that say if a bill came to the floor this afternoon to simply raise the debt limit without any other provisions to it, there's a number of people who would say vote no. I would vote no."

Garrett also seemed to downplay how financial markets might react to a failure to reach an agreement to raise the debt ceiling.

"I think the markets are pretty intelligent with regard to this," he said. "They know that Congress needs to grapple with this and they know that Congress and the White House will. But the markets are also looking for us to put the federal budget on a sustainable path as well.

"I think if the Fed chairman were sitting with us right now, he would agree that we need to not only grapple with the debt limit, but we need to grapple with the fact that we are spending more money than we're taking in," Garrett added.