WASHINGTON » President Barack Obama warned Republicans today against picking another fight over the nation’s debt ceiling, telling business leaders that it’s “not a game that I will play.”

Obama said in remarks to the Business Roundtable that he was aware of reports that Republicans may be willing to agree to higher tax rates on the wealthy as a way to avert the looming “fiscal cliff” and then come back next year with more leverage 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.”

The president cited the prolonged and deeply partisan standoff over raising the U.S. debt limit last year that led the nation to the brink of default for the first time in its history. The move prompted Standard & Poor’s to take the drastic step of stripping the government of its “AAA” rating on its bonds, a sign of the toll of the political debacle.

Obama’s cautionary tone to congressional Republicans came amid a continuing standoff over the looming fiscal cliff, a series of automatic spending cuts and tax increases scheduled for the end of the year that could undermine the nation’s economic recovery. Negotiations have focused on whether tax rates for the wealthy should increase, how deeply to cut spending on entitlements such as Medicare and how to deal with raising the government’s borrowing limit early next year.

If Congress and the White House don’t reach a budget deal, about $1.2 trillion in spending cuts and tax increases will automatically kick in starting Jan. 2, a scenario that’s been dubbed the “fiscal cliff,” because it is likely to send the economy back into recession and drive up unemployment.

Meantime, House Speaker John Boehner, R-Ohio, and Republican leaders said today — prior to Obama’s remarks — that the White House had failed to offer a “balanced approach” that had a chance of clearing either chamber of Congress. “We can’t negotiate with ourselves,” Boehner said.

House Majority Leader Eric Cantor, R-Va., said Republicans want to “sit down with the president. We want to talk specifics. We put an offer on the table. Now he has out of hand rejected that. Where are the specifics? Where are the discussions? Nothing is going on. Meanwhile, the people of this country are the ones that suffer.”

House Republicans have proposed a 10-year, $2.2 trillion blueprint that calls for increasing the eligibility age for Medicare and lowering cost-of-living hikes for Social Security benefits. It came in response to Obama’s offer last week to boost taxes by $1.6 trillion over the coming decade but largely exempt Medicare and Social Security from budget cuts.

The White House has ridiculed Boehner’s approach as nothing more than “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. Congressional Republicans say Obama has focused only on tax increases but not offered enough specifics on reducing spending.

Obama told business leaders that his economic showdown with House Republicans could be solved quickly if the GOP would accept that raising tax rates on the wealthiest Americans is the only viable way to raise the money needed for a fair debt reduction plan.

“The numbers actually aren’t that far apart,” Obama said. “Another way of putting this is: We can probably solve this in about a week. It’s not that tough. But we need that conceptual breakthrough.”

Republicans dispute Obama’s assertion and have proposed capping deductions and changing the tax code in other ways to generate the tax money.