The "fiscal cliff," with its year-end deadline, refers to increases that would affect every worker who pays federal income tax, as well as spending cuts that would begin to bite defense and domestic programs alike. Economists in and out of government say the combination carries the risk of a new recession, at a time the economy is still struggling to recover fully from the worst slowdown in decades.
Obama delivered his latest warning at the meeting of the Business Roundtable a few blocks from the White House.
He said he was aware of reports that Republicans may be willing to agree to higher tax rates on the wealthy, then seek to extract spending cuts from the White House in exchange for raising the government's borrowing limit.
"That is a bad strategy for America, it's a bad strategy for your businesses and it's not a game that I will play," Obama said, recalling the "catastrophe that happened in August of 2011."
That was a reference to a partisan standoff that led the Treasury to the brink of the nation's first-ever default and prompted Standard & Poor's to reduce the rating for government bonds.
Avoiding that crisis led directly to the current standoff, since part of the compromise then was to set in motion the spending cuts that Obama and Congress are now trying to avoid.
Coburn, a conservative rebel within the GOP ranks, made it clear months ago he was ready to support higher tax revenue as part of an overall deal to restrain government spending programs.
In an interview on MSNBC, he went one step further.
"I don't really care which way we do it," he said. "Actually, I would rather see the rates go up than do it the other way because it gives us greater chance to reform the tax code and broaden the base in the future."
Sen. Chuck Schumer, D-N.Y., taunted members of the House GOP leadership. They are "like generals, hunkered away in a bunker, who don't realize that their army in the field has already laid down its arms," he said.
A handful of other Republicans in both houses have said in recent days they could support raising the top tax rates. In the House, conservatives say they suspect House Speaker John Boehner let it be known he wouldn't mind the discussion, even though he made a case in a closed-door meeting of the rank and file last week that raising rates would be worse for the economy than raising revenue by closing tax loopholes.
House Republicans opened the week by proposing a deficit reduction plan that includes raising $800 billion in higher revenue and curtailing cost-of-living increases for Social Security and other government benefit programs as part of a plan to cut deficits by $2.2 trillion over a decade.
In addition, they recommended raising the age of eligibility for Medicare beginning in a decade, a step that generates no savings in the next 10 years but makes longer-term changes that would strengthen the program's financial foundation.
The White House ridiculed that plan as "magic beans and fairy dust," saying taxes must rise on families earning $250,000 or more to generate enough revenue to deal with the nation's fiscal crisis.
Associated Press writers Jim Kuhnhenn and Andrew Taylor contributed to this story.