WASHINGTON (AP) — In a chilling forecast, the White House is predicting a 10-year federal deficit of $9 trillion — more than the sum of all previous deficits since America’s founding. And it says by the next decade’s end the national debt will equal three-quarters of the entire U.S. economy.

But before President Obama can do much about it, he’ll have to weather recession aftershocks including unemployment that his advisers said Tuesday is still heading for 10 percent.

Overall, White House and congressional budget analysts said in a brace of new estimates that the economy will shrink by 2.5 to 2.8 percent this year even as it begins to climb out of the recession. Those estimates reflect this year’s deeper-than-expected economic plunge.

The grim deficit news presents Obama with both immediate and longer-term challenges. The still fragile economy cannot afford deficit-fighting cures such as spending cuts or tax increases. But nervous holders of U.S. debt, particularly foreign bondholders, could demand interest rate increases that would quickly be felt in the pocketbooks of American consumers.

Amid the gloomy numbers on Tuesday, Obama signaled his satisfaction with improvements in the economy by announcing he would nominate Republican Ben Bernanke to a second term as chairman of the Federal Reserve.

The announcement, welcomed on Wall Street, diverted attention from the budget news and helped neutralize any disturbance in the financial markets from the high deficit projections.

The White House Office of Management and Budget indicated that the president will have to struggle to meet his vow of cutting the deficit in half in 2013 — a promise that earlier budget projections suggested he could accomplish with ease.

‘‘This recession was simply worse than the information that we and other forecasters had back in last fall and early this winter,’’ said Obama economic adviser Christina Romer.

The deficit numbers also could complicate Obama’s drive to persuade Congress to enact a major overhaul of the health care system — one that could cost $1 trillion or more over 10 years. Obama has said he doesn’t want the measure to add to the deficit, but lawmakers have been unable to agree on revenues that would cover the cost.

What’s more, the high unemployment is expected to last well into the congressional election campaign next year, turning the contests into a referendum on Obama’s economic policies.

Republicans were ready to pounce.

‘‘The alarm bells on our nation’s fiscal condition have now become a siren,’’ said Senate Minority Leader Mitch McConnell of Kentucky. ‘‘If anyone had any doubts that this burden on future generations is unsustainable, they’re gone — spending, borrowing and debt are out of control.’’

Even supporters of Obama’s economic policies said the long-term outlook places the federal government on an unsustainable path that will force the president and Congress to consider politically unpopular measures, including tax increases and cuts in government programs.

‘‘The numbers today portend the biggest budget fight we’ve probably had in decades in the United States,’’ said Stan Collender, a former congressional budget official.

The summer analyses by the White House budget office and by the Congressional Budget Office reached similarly bleak conclusions. The CBO’s 10-year deficit figure was smaller — $7 trillion — but that is because it assumes that all tax cuts put into place in the administration of former President George W. Bush will expire on schedule by 2011. Obama’s budget baseline, however, hews to his proposal to keep the tax cuts in place for families earning less than $250,000 a year.

Both budget offices see the national debt — the accumulation of annual budget deficits — as more than doubling over the next decade. The public national debt, made up of amounts the government owes to the public, including foreign governments, stood Tuesday at a staggering $7.4 trillion. White House budget officials predicted it would reach $17.5 trillion in 2019, or 76.5 percent of the gross domestic product. That would be the highest proportion in six decades.

Congressional Budget Office director Douglas Elmendorf said if Congress doesn’t reduce deficits, interest rates are likely to rise, hurting the economy. But if Congress acts too soon, the economic recovery — once it arrives — could be thwarted.

‘‘We face perils in acting and perils in not acting,’’ Elmendorf told reporters.

David Walker, former head of the Government Accountability Office, said the numbers illustrated the need for a national commission that would review spending and taxing options and present lawmakers with a deficit reduction plan that Congress could approve or reject.

‘‘We’re going to have to do a hard course correction once we turn the corner on the economy,’’ Walker, now president and CEO of the Peter G. Peterson Foundation, said.

Both Romer and Obama budget director Peter Orszag said this year’s contraction would have been far worse without money from the $787 billion economic stimulus package that the president pushed through Congress as one of his first major acts.

At the same time, the continuing stresses on the economy have, in effect, increased the size of the stimulus package because the government will have to spend more in unemployment insurance and food stamps, Orszag said. He said the cost of the stimulus package — which spends most of its money in fiscal year 2010 — will grow by tens of billions of dollars above the original $787 billion.

The White House also credited the $3 billion cash-for-clunkers auto program for contributing to recent economic growth.

Orszag, anticipating backlash over the deficit numbers, conceded that the long-term deficits are ‘‘higher than desirable.’’ The annual negative balances amount to about 4 percent of the gross domestic product, a number that many economists say is unsustainable.

But Orszag also argued that overhauling the health system would reduce health care costs and address the biggest contributor to higher deficits.

‘‘I know there are going to be some who say that this report proves that we can’t afford health reform,’’ he said. ‘‘I think that has it backward.’’

At the same time, 10-year budget projections can be ‘‘wildly inaccurate,’’ said Collender, now a partner at Qorvis Communications. Collender noted that there will be five congressional elections over the next 10 years and any number of foreign and domestic challenges that will make actual deficit figures very different from the estimates.

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Associated Press writers Christopher S. Rugaber, Tom Raum and Stephen Ohlemacher contributed to this report.