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President Barack Obama's administration will "absolutely" let the United States fall off the fiscal cliff as scheduled, unless Republicans give in to his Obama's demand to raise tax rates at upper income levels, Treasury Secretary Timothy Geithner said Wednesday.

"The size of the problem is so large it can't be solved without rates going up," Geithner told CNBC.

The tough line comes as Obama resumes contact with House Speaker John Boehner over ways to avert across-the-board spending cuts and tax increases at the turn of the year.

Geithner's comments drew a fierce response from Republicans. Sen. Orrin Hatch of Utah called his statement "stunning and irresponsible." He added, "Going over the fiscal cliff will put our economy, jobs, people's paychecks and retirement at risk, but that is what the White House wants, according to Secretary Geithner, if they don't get their way."

Economists inside and outside the government warn that failing to reach agreement on taxes and spending could land the economy back in recession.

It wasn't the only demand from the administration on a day Obama telephoned Boehner, the first known discussion of the fiscal cliff between the two in several days. Appearing before corporate CEOs, the president warned Republicans not to inject the threat of a government default into negotiations over the fiscal cliff as a way of extracting concessions on spending cuts. "It's not a game I will play," he said, recalling the brinkmanship of last year in which a budget standoff pushed the Treasury to the edge of a first-ever default.

Obama will visit a northern Virginia family on Thursday to highlight his call for extending current tax rates to all but the top 2 percent of earners. The White House said a member of the family wanted to "share her story about how paying $2,200 more in taxes next year would impact them if Congress doesn't act."

Both sides say they want a compromise, although the administration's hand in bargaining is strengthened by polls showing public support for Obama's position on taxes, as well as by his re-election last month. The president is also working to rally the public to his side and has a trip scheduled to Detroit next week.

In a concession, Republican leaders have agreed to back increased tax revenue. Yet despite defections from within the rank and file, they have so far balked at Obama's demand that rates go up on income over $200,000 for individuals and $250,000 for couples. They have also called for spending cuts and measures to slow the growth of government benefit programs. Earlier this week, they called for curbing the growth in Social Security cost-of-living increases, as well as delaying Medicare eligibility from 65 to 67, beginning in a decade.

Obama has said he will back spending cuts, including savings in Medicare, as part of a deal that includes the tax proposal that was a key part of re-election bid.

Once Republicans yield on taxes, he told the Business Roundtable, "We can probably solve this in about a week; it's not that tough."

Republicans argue that they can raise about $800 billion in additional government revenue over a decade by closing loopholes and narrowing tax deductions on the wealthy, rather than raising income tax rates. They argue the rate increase would impose a particularly harmful impact on the economy and job creation at a time when the country is still struggling to recover fully from the deepest recession in decades.

Reporting by The Associated Press.

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