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The GOP field’s targets aren’t accidents.

In the roughly six decades since the end of World War II, government spending has averaged about 20 percent of GDP while taxes have averaged about 18 percent — thus the persistent but small deficit.

This year, though, federal revenue is just 14.8 percent of GDP while spending is 24.1 percent. The resulting gap is the reason for the $1.3 trillion deficit that the government reported for fiscal 2011.

The problem with Republicans’ goals, though, is that more spending is already built into the future with the aging population.

“If you are going to keep spending at 20 percent of GDP, you are going to have to find a way to cut other spending by that much to offset the growth of Social Security, Medicare and Medicaid,” Mr. Bixby said. “If you are going to cut 5 or 6 percent of GDP out of discretionary programs, that means cutting about 75 percent of what we spend on everything else — all the appropriations, including defense.”

Mr. Obama has defended increased spending in the short term, but says the country must lower deficits and bring the debt under control in the long term.

Still, he envisions much higher spending than Republicans. The budget he submitted in February called for spending to hover between 23 percent and 24 percent of GDP for the next decade — a level substantially higher than the GOP has proposed.

Mr. Obama has called for increased taxes to bridge some of the gap, though his budget would show significant deficits every year for the next decade.

Ben LaBolt, a spokesman for the Obama 2012 re-election campaign, said the Republicans’ plans seek to balance the budget “on the backs of seniors and the middle class — ending Medicare as we know it, gutting Social Security, and eliminating the investments necessary to create the jobs of the future.”

“The president has proposed a balanced plan that would shrink the deficit by $4 trillion by asking everyone to do their fair share and ensuring that the plan helps, not hinders, growth,” Mr. LaBolt said.

In December, the president’s fiscal commission recommended that Congress cap spending at 21 percent of GDP by 2020, and increase taxes to the same level.

Now a 12-member congressional supercommittee has been tasked with identifying at least $1.2 trillion in savings or new tax revenue before a Thanksgiving deadline. Failure would trigger $1.2 trillion in automatic spending cuts to a wide range of domestic programs and the Pentagon.

The effort has spilled into the presidential campaign. Republican candidates have ridiculed the committee while batting around respective economic plans centered on the GDP.

Each of the Republican candidates’ plans generally sets forward lower spending targets while embracing the notion of reshaping entitlement programs to save money. But they tend to gloss over specific changes they would make to Social Security, Medicare and Medicaid — and the fact that the real cost savings from gradually increasing the retirement age or means testing the programs would appear outside the 10-year budget cycle.

“You are certainly not going to get big savings this decade,” Mr. Bixby said. “That doesn’t mean you shouldn’t do it because you want to get the savings in the out years.”