Rep. Lee Terry, R-Neb., signed Norquist's pledge but says now that he's open to a deal that includes some new tax revenues. Still, he said, the president needs to work across the aisle.

“He's not dealing with terrorists, he's dealing with Republicans who don't want to raise taxes,” Terry said.

Terry said Obama has an incentive to allow the country to go over the cliff and then blame Republicans.

“We're screwed either way,” Terry said. “We really have no leverage in these discussions.”