The challenge confronting Republicans who could be open to higher taxes was evident this week in remarks by Chambliss, who with Coburn is part of the Senate’s bipartisan “Gang of Six” working on a deficit-reduction plan.

“You can’t solve this debt problem with just reductions in discretionary spending,” the senator from Georgia told CNN. “You can’t solve it just by attacking and reforming entitlements. You’ve got to look at the revenue side also.”

Chambliss said the group was looking at reductions in overall rates for people and businesses coupled with the elimination of “tax expenditures,” a term that refers to breaks and loopholes.

“If we don’t want to pay the debt back, then we could just not worry about the revenues, but the fact is we’ve got a $14 trillion debt staring us in the face and revenue has to be on the table if we’re serious about attacking that debt,” Chambliss told the network.

Still, after Obama’s speech, Cham­bliss said he was “disappointed to hear the president advocate for tax increases.”