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“The president has failed to offer a single serious idea to save Social Security and is the only president in modern history to cut Medicare benefits for seniors,” the former Massachusetts governor said in a statement.

The president’s budget request for fiscal 2013 anticipates borrowing a total of $901 billion, which would be the first time since Mr. Obama took office that the deficit falls below $1 trillion. But the spending plan pegs the deficit for the current fiscal year, which ends Sept. 30, at $1.33 trillion, nearly the same level it was three years after the president promised to cut it in half by the end of 2012.

Administration officials say the budget will reduce the deficit $4 trillion over the next 10 years through a mix of tax increases, caps on spending and savings in other areas.

“I’m proposing some difficult cuts that, frankly, I wouldn’t ordinarily make,” the president said. He said the reducing the deficit in the long term will allow his administration to boost the economy right now.

But Republicans say the budget also relies on an accounting trick to count hundreds of billions of dollars in savings tied to the drawdown of the war in Iraq. Rather than apply all of the $850 billion of presumed savings to deficit reduction, Mr. Obama intends to spend half of it on infrastructure projects to create jobs.

Sen. Jeff Sessions, Alabama Republican and ranking member of the Senate Budget Committee, said Mr. Obama’s 10-year plan would add $11.2 trillion to the national debt, little changed from the projected $11.5 trillion under currently enacted spending legislation.

“It’s a tax-and-spend budget, virtually identical to the path we were already on,” Mr. Sessions said. “Where is the $4 trillion in deficit reduction?”

Referring to a debt crisis that has spawned civil turmoil abroad, Mr. Sessions added, “Next year, the United States could be like Greece.”

Former U.S. Comptroller General David A. Walker said Mr. Obama’s budget will add $6.684 trillion in deficits over the next decade and predicted that revenue increases will outpace spending cuts. He also criticized the administration’s practice of counting reductions in military spending overseas as long-term “savings.”

“The president’s budget fails to lay out a substantive path to restore fiscal sanity,” Mr. Walker said in a statement.

Sen. Mark L. Pryor, Arkansas Democrat, said Mr. Obama’s budget is a case of misplaced priorities that he wouldn’t support.

“I am concerned that spending on luxury programs, such as high-speed rail and spaceship taxis, take precedence over basic needs,” Mr. Pryor said in a statement. “… Moreover, some of the nation’s best and most cost-effective military units have been targeted for cuts. I will not support a budget that sidelines basic needs, invests in luxuries and still results in a whopping $700 billion deficit in 2022.”

The president’s proposal forecasts a high level of government spending indefinitely. The plan calls for overall government spending to remain above 22 percent of gross domestic product for the next decade. Overall government spending has averaged about 20 percent of GDP in the post-World War II era.

The budget calls for a 10-year, $60 billion “financial crisis responsibility fee” on the nation’s biggest banks, aimed at recovering the costs of the financial bailout and helping homeowners facing foreclosure. It would raise $41 billion over 10 years by eliminating tax breaks for oil, gas and coal companies.

Spending would be reduced in several Cabinet agencies. The Pentagon’s core budget would decrease for the first time since 1998 by 1 percent. But the president also would boost spending slightly at the State Department, including a new $770 million fund to promote democratic and economic reforms in the Middle East and North Africa. He also would keep military aid to Egypt at $1.3 billion, in spite of a crisis triggered by an Egyptian crackdown against American democracy activists.

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