If Republicans agree to Obama's plan to increase rates on the top 2% of Americans, Corker added, "the focus then shifts to entitlements and maybe it puts us in a place where we actually can do something that really saves the nation."
Besides getting tax hikes through the Republican-dominated House, Corker's proposal faces another hurdle: Democrats haven't been receptive to GOP proposals on the entitlement programs. Senate Democratic Whip Dick Durbin, (D., Ill.) on Sunday was skeptical about proposals to increase the eligibility age for Medicare from 65 to 67. He said he doesn't see Congress addressing the complicated issue of Medicare overhaul in the three weeks remaining before the end of the year.
"I just don't think we can do it in a matter of days here before the end of the year," Durbin said. "We need to address that in a thoughtful way through the committee structure after the first of the year."
And hard-line fiscal conservatives in the House are holding fast to their position.
"No Republican wants to vote for a rate tax increase," said Rep. Jeb Hensarling (R., Texas) chairman of the House Republican Conference.
Added Rep. Marsha Blackburn (R., Tenn.): "I'm not sure there is support for the rate hikes. There is support for revenue by cleaning up the code."
Still, at least one House Republican has said there is another way. Rep. Tom Cole, of Oklahoma, has said Obama and Boehner should agree not to raise tax rates on the majority of Americans and negotiate the rates for top earners later. Cole said Sunday that most House Republicans would vote for that approach because it doesn't include a rate hike.
"You know, it's not waving a white flag to recognize political reality," Cole said.
Sen. Tom Coburn, (R., Okla.) already has said he could support higher tax rates on upper incomes as part of a comprehensive plan to cut the federal deficit.
When asked Sunday what it would take to sign on to a tax rate increase, Coburn echoed Corker's comments by responding, "Significant entitlement reform." He quickly added, however, that he has estimated that such a tax rate increase would only affect about 7% of the deficit.