Clyburn: Deficit deal likely under the gun

But Clyburn’s comments also illustrated how difficult it might be for the two parties to agree on a deficit package, even though Biden has said the current talks are on track to find $1 trillion in deficit cuts.

The South Carolina Democrat told Bloomberg that new tax-related revenue would have to be part of any deal. For their part, top Republicans in both chambers — including Sen. Jon Kyl of Arizona and Rep. Eric CantorEric Ivan CantorFeehery: The governing party 'Release the memo' — let's stop pretending that Democrats are the defenders of the FBI Raúl Labrador, a model for Hispanic politicians reaching higher MORE of Virginia, the two Republicans taking part in the talks with Biden — have said that is off the table.

“I don’t think they’re posturing at all. I think they are speaking to what seems to be the sentiment of their caucus,” Clyburn said. “But I do believe that, sometime between now and the first of August, everybody will come to the realization that this cannot be done without revenue raisers.”

At the same time, Clyburn did not seem too interested in tackling Medicare in the current talks, either. “We are not going to reduce benefits at all,” he said. 

And while Clyburn talked about dealing with the Bush tax cuts and the estate tax in the current talks, he also said that revenues could be raised through tax reform.

But his idea — reducing the top corporate tax rate from 35 percent to 26 while getting rid of tax credits and deductions — would conceivably face several challenges.

For one, while Treasury Secretary Timothy Geithner has said that tax reform would be put on the backburner until the debt-ceiling issue is dealt with, the Obama administration has also called for a corporate tax overhaul that neither adds nor subtracts from the deficit.

Meanwhile, a 2007 Treasury Department study found that eliminating a wide range of tax credits and deductions would only be able to pay for reducing the top corporate rate to 28 percent.