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 percent of the deficit.
"Will I accept a tax increase as a part of a deal to actually solve our problems? Yes," Coburn said. "But the president's negotiating with the wrong people. He needs to be negotiating with our bondholders in China, because if we don't put a credible plan on the discussion, ultimately, we all lose."
Obama's plan would raise $1.6 trillion in revenue over 10 years, partly by letting decade-old tax cuts on the country's highest earners expire at the end of the year. He would continue those Bush-era tax cuts for everyone except individuals earning more than $200,000 and couples making above $250,000. The highest rates on top-paid Americans would rise from 33 percent and 35 percent to 36 percent and 39.6 percent.
Boehner has offered $800 billion in new revenues to be raised by reducing or eliminating unspecified tax breaks on upper-income people. The Republican plan would cut spending by $1.4 trillion, including by trimming annual increases in Social Security payments and raising the eligibility age for Medicare.
Hensarling and Coburn spoke on ABC's "This Week." Blackburn and Cole spoke on CNN's "State of the Union." Durbin spoke on NBC's "Meet the Press."