Officials provided no details of the conversation, which came on the same day the president, hewing to a hard line, publicly warned congressional Republicans not to inject the threat of a government default into the already complex issue.
"It's not a game I will play," Obama told a group of business leaders as Republicans struggled to find their footing in talks with a recently re-elected president and unified congressional Democrats.
Among the Republicans, Sen. Tom Coburn of Oklahoma became the latest to break ranks and say he could support Obama's demand for an increase in tax rates at upper incomes as part of a comprehensive plan to cut federal deficits.
Across the Capitol, House Majority Leader Eric Cantor said Republicans want to "sit down with the president. We want to talk specifics." He noted that the GOP had made a compromise offer earlier in the week and the White House had rejected it.
Officials said after the talk between Obama and Boehner, R-Ohio, there was no immediate plan for a resumption of negotiations to avert the cliff. At the same time, they said that for the first time in a few days, at least one top presidential aide had been in touch with Republicans by email on the subject.
Each side has been declaring that the crisis can be averted if the other will give ground.
"We can probably solve this in about a week, it's not that tough," Obama said in lunchtime remarks to the Business Roundtable.
It has been several days since either the president or congressional Democrats signaled any interest in negotiations that both sides say are essential to a compromise. Presidential aides have even encouraged speculation that Obama is willing to let the economy go over the "fiscal cliff" if necessary and gamble that the public blames Republicans for any fallout.
Eventually, Democrats acknowledge, there will be compromise talks, possibly quite soon, toward an agreement that raises revenues, reins in Medicare and other government benefit programs, and perhaps raises the government's $16.4 trillion borrowing limit.
For now, the demonstration of presidential inflexibility appears designed to show that, unlike two years ago, Obama will refuse to sign legislation extending top-rate tax cuts and also to allow public and private pressure to build on the Republican leadership.
Treasury Secretary Tim Geithner underscored the president's determination when he told CNBC the administration was "absolutely" prepared to have the economy go over the so-called cliff if its terms aren't met. "The size of the problem is so large that it can't be solved without rates going up," he said.
So far, the GOP has offered to support non-specified increases to raise tax revenues by $800 billion over a decade but has rejected Obama's demand to let the top income tax rate rise from 35 percent to 39.6 percent.
To buttress their case, Republican officials in Congress pointed to numerous proposals that Obama has previously advanced that could generate the same amount of revenue he is seeking — without raising rates. The list includes limiting the tax deductions taken by upper-income taxpayers, raising taxes on the oil and gas industry and curbing or eliminating the deductibility of tax-exempt bonds.
Separately, in a bit of political theater, Senate Republican leader Mitch McConnell urged Democrats to allow a vote on Obama's current plan, which calls for a $1.6 trillion tax increase over a decade, in an attempt to show it lacks support.
The majority leader, Democratic Sen. Harry Reid of Nevada, refused.
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.
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