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As the sequester spending cuts begin to take effect, the White House today pointed to one potential silver lining: significant progress in the battle to tame the nation's deficit and debt.

"The 'big deal' has been partly accomplished," declared White House spokesman Jay Carney, when asked whether President Obama still had hopes for a sweeping deficit reduction compromise with Republicans.

Indeed, Obama and Congress have already signed into law roughly $2.5 trillion in savings over the next decade, including the so-called $1.2 trillion sequester cuts, more than $600 billion in new tax revenue and $400 billion in interest savings.

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It's more than halfway to the $4 trillion goal set out by Obama's fiscal commission and embraced by both parties in August 2010.

So, what's left to be done? "It may be the 'petit bargain,' I guess," Carney joked today. "If you, you know, go all French."

Enter a prominent bipartisan group of debt and deficit experts, who aren't laughing.

"If they won't go big, we shouldn't go petit," Maya MacGuineas, president of the Committee for a Responsible Federal Budget, told ABC News. "At least we could go medium."

MacGuineas, who also heads the Fix the Debt campaign co-founded by Obama fiscal commission chairmen Erskine Bowles and Alan Simpson, said in the two years since policymakers set their $4 trillion goal things have gotten worse.

The magic number to trim is now closer to $6.5 trillion over a decade, she said.

"It's jaw-dropping. It's a painful reaction of when you wait to take action, the costs go up," MacGuineas said. "That's the amount of cuts it would take to bring us to the same level, putting our debt on a downward path."

More sobering: There's little sign Obama and Congress will compromise to address the biggest drivers of U.S. debt.

"They haven't done any of the tough stuff, any of the important stuff, they haven't reformed the tax code," Bowles told ABC News' Jonathan Karl last month. "They haven't done anything to slow the rate of health care to the rate of growth of the economy, they haven't made Social Security sustainably solvent."

Obama says he has a plan on the table to trim an additional $1.8 trillion from the deficit over the next decade through a combination of tax code reforms and changes to entitlement programs. Experts say it would be a step forward but not nearly enough to celebrate.

"We support any plan that's big enough to fix the problem. His plan isn't," MacGuineas said. "But you could super-size it."