President Obama flatly rejected Republicans’ offer on avoiding the fiscal cliff Tuesday, saying that it doesn’t go far enough in raising taxes to reduce the budget deficit significantly over the next decade.

The main sticking point between the White House and House Republicans continues to be Mr. Obama’s proposal to end the Bush-era tax cuts on the wealthiest Americans, with Republicans arguing that a tax increase would hurt the economy and that the lost revenue can be raised in other ways — from closing loopholes and deductions on high earners.

But the White House disagrees, saying he is unwilling to limit two tax write-offs: deductions for charitable donations and for the interest homeowners pay on their mortgages.

“What I’m going to need … is an acknowledgment that folks like me can pay a little bit higher rate,” he told Bloomberg on Tuesday in his first sit-down television interview since his re-election.

Mr. Obama reasserted his position the day after House Speaker John A. Boehner, Ohio Republican, proposed $2.2 trillion in spending cuts and new revenue over the next decade — a plan that produces the revenue by closing loopholes and eliminating deductions, not through higher tax rates.

Even though the two sides are still far apart, the president said a deal can still be done by Dec. 31, the deadline Washington faces to hash out a budget agreement or fall over the “fiscal cliff” — a scheduled double hit of the Bush tax cuts’ expiration and automatic across-the-board spending cuts.

“We’re going to have higher rates for the wealthiest,” Mr. Obama said. “It’s just a matter of math.”

Some budget analysts disagree and say coming up with enough revenue to start paying down the nation’s debt depends on how you rewrite the tax code.

The nonpartisan Center for a Responsible Federal Budget recently released a report pointing to some simple tax changes that would raise the same amount of revenue as letting the upper-income tax cuts expire.

Among other ideas, the budget center advocates placing a cap on itemized deductions for wealthy Americans — something the Obama plan includes. The reports also calls for limiting the combined value of various deductions, credits and exclusions for high earners.

Alice Rivlin, a member of Mr. Obama’s fiscal commission and the director of the Office of Management and Budget under President Clinton, has said any tax increase should be postponed. In June, she testified before the Senate Finance Committee that all of the Bush-era taxes should be extended until Washington can overhaul the tax code and make cuts to entitlement programs.

With talks still stalled, both sides have spent the past day and a half accusing each other of failing to provide specifics on the part of the deal least palatable to their side.

The president last week outlined a plan that calls for a $1.6 trillion tax increase over the next decade, $50 billion in new stimulus spending in 2013, and a change that would transfer from Congress to the White House the power to raise the federal debt limit.

Republicans say their offer, which includes $800 billion in tax increases achieved through eliminating certain targeted tax benefits for the wealthy, is a serious effort to find middle ground, considering most Republicans oppose any type of tax increase.

“With our latest offer, we have demonstrated there is a middle-ground solution that can cut spending and bring in revenue without hurting American small businesses,” Mr. Boehner said. “The president now has an obligation to respond with a proposal that does the same.”

Mr. Boehner has called last week’s proposal from the White House a “la-la-land offer” that asked for $1.6 trillion in new taxes and up to $400 billion in potential spending cuts without a detailed plan to rein in entitlement spending.

White House spokesman Jay Carney later Tuesday said Republicans only submitted “a couple of bullet points” with “no specificity whatsoever,” not a detailed offer that included exactly which deductions and loopholes they would eliminate.

“We don’t know who pays. We don’t know what kind of legislation it would produce. We don’t know what we’re talking about,” he said. “It’s magic beans and fairy dust.”

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