Show host Chris Wallace responded: "You would allow the Ex-Im Bank to expire in September?"
McCarthy replied, "Yes, because it's something that the private sector can be able to do."
The Export-Import Bank makes loan guarantees to foreign buyers who want to purchase from U.S. exporters. Many conservatives oppose it and say it amounts to "corporate welfare."
When Congress voted to reauthorize the agency in 2012, McCarthy was among the lawmakers who voted in favor of it.
McCarthy was elected the House majority leader last week, making him the second-ranking Republican in the lower chamber.