Rep. Mick Mulvaney (R-S.C.) said Monday that members of Congress are working in private on a deal to cut the deficit by $2.5 trillion over the next decade.

Mulvaney told WRHI radio in South Carolina that while the two parties are still openly deadlocked on the issue of spending cuts versus raising taxes, he thinks they are making progress.

"It's amazing when you close the door and folks are willing to talk privately about things how reasonable some Democrats can be in terms of reforming entitlement programs and how Republicans can be in terms of, say, reforming the tax code," Mulvaney said.

Mulvaney did not reveal which members are negotiating and said the group has no formal name. But he said many Democrats have a real interest in cutting the budget deficit and the national debt, which has risen to $17.2 trillion.

"I have real hard-core, left-wing Democrat friends who are afraid of the deficit," he said. "They want to fix it in a way slightly different than I do. That's fine, as long as they're convinced that it's the risk that it is."

The Budget Control Act (BCA) of 2011 was originally designed to cut $2.5 trillion from the deficit. But the budget deal reached just before Christmas altered the BCA by moving more of the cuts into the future and raising revenue by increasing customs user fees and safety fees for air passengers.

A deal on entitlements might be needed in the coming weeks, because the government will lose its authority to borrow more money as of Feb. 7. Republicans argue that another increase in the debt ceiling should happen only as part of an agreement to cut an equal amount of spending, but President Obama has again vowed not to negotiate.