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Republicans faulted Mr. Obama for not going far enough in his $3.7 trillion 2012 budget proposal to rein in near-term deficits and long-term debt. Democrats defended the plan as a solid first step.

The blueprint, which the president sent to Congress on Feb. 14, calls for a five-year freeze on non-security discretionary spending, reducing the projected deficit an estimated $400 billion over the next decade. Mr. Obama said it makes “tough decisions” by trimming popular government programs including Pell Grants and heating assistance for the poor, but he attracted criticism for not addressing entitlement programs, which are the biggest drivers of long-term federal deficits.

Mr. Ryan on Sunday promised that the Republican budget would tackle entitlements and lead where Mr. Obama “chose not to,” but he didn’t offer additional details on the plan.

In a potentially embarrassing moment for the White House on Sunday, the bipartisan co-chairmen of the fiscal panel that Mr. Obama created criticized his budget in a Washington Post opinion column.

“To be sure, the president’s budget doesn’t go nearly far enough in addressing the nation’s fiscal challenges. In fact, it goes nowhere close,” wrote Clinton White House Chief of Staff Erskine Bowles and former Sen. Alan Simpson, Wyoming Republican.

A majority of the panel’s 18 members approved a sweeping austerity plan in December, but it failed to garner enough votes for automatic congressional consideration. Through a mixture of tax hikes and spending cuts, the proposal called for reducing the projected deficit by $4 trillion over 10 years.