President Obama unveiled a $3.8 trillion spending plan on Monday for 2013 and a 10-year vision that seeks to cut $4 trillion from the overall deficit, but does little to restrain growth in the U.S. government's huge entitlement programs and adds $6.6 trillion in deficits over 10 years.

In his 10-year projection, the annual deficit falls below $600 billion just once — in 2018. The $6.6 trillion is added on top of the president's recent additions to the federal debt — the $15.36 trillion national debt is now greater than the annual gross domestic product.

In his long-term vision, sure to be central to his reelection campaign, the president would achieve $1.5 trillion of deficit reductions by raising current tax rates on high-income Americans and removing certain corporate tax breaks. The other $1.5 trillion comes from spending cuts over the decade.

"Right now, we're scheduled to spend nearly $1 trillion more on what was intended to be a temporary tax cut for the wealthiest 2 percent of Americans," Obama told an audience in Annandale, Va., on Monday. "That's very expensive ... Keep in mind that a quarter of millionaires pay lower tax rates than millions of middle class households."

Republicans immediately rejected Obama's new budget as a retread of previously rejected ideas, and noted that his own Democratic Party hasn't introduced a budget in the Senate in three years.

Alabama Sen. Jeff Sessions, ranking Republican on the Senate Banking Committee, added that the president's math is very fuzzy.

"The president claims that his fiscal plan will reduce the deficit by $4 trillion over the next 10 years, including the previously enacted $1 trillion Budget Control Act cuts that are part of current law. An honest analysis reveals, however, that the president's budget would only reduce the deficit by about $300 billion in comparison to what was agreed to in the Budget Control Act last August. In other words, the White House has utterly failed to meet even the minimum target they have identified as necessary," Sessions said in a statement.

Obama's budget, while requesting substantial spending increases on infrastructure and job training, also takes $30 billion from Medicare to pay for other programs, say Republicans, who note Medicare is already close to broke. In all, entitlement spending consumes 40 percent of the annual budget.

"This budget does nothing to prevent the bankruptcy of critical programs, threatening the health and retirement security of current and future seniors," House Budget Committee Chairman Paul Ryan said in a statement. "The broken promises and recycled gimmicks contained in this budget have dramatically widened this president's growing credibility deficit."

But House Democratic Leader Nancy Pelosi called it a commitment to "reigniting the American dream and building ladders of opportunity."

Preceding the president's appearance at Northern Virginia Community College, where he offered his opening bid, a fact sheet previewing the budget sought to cast the impending debate as a battle to protect the middle class, which is losing steam against a wealthy upper crust.

But in his budget message, Obama rejected claims that he is engaging in class warfare.

"This is not about class warfare. This is about the nation's welfare," he said.

The president, who joked that he'd visited the NVCC campus so often, he's three credits shy of a degree, told students that Congress must act to make permanent a tuition tax credit, needs to prevent interest rates from going up on student loans and has an obligation to extend the payroll tax cut.

"The last thing we need is for Washington to stand in the way of America's comeback. What does that mean? For starters, it means Congress must stop taxes from going up on 160 million Americans by the end of this month," he said.

His proposals include a new $8 billion "Community College to Career Fund, which seeks to help forge new partnerships between community colleges and businesses to train 2 million workers for good-paying jobs in high-growth and high-demand industries. It also seeks to provide funding for community colleges and states to partner with businesses to train workers in areas such as health care, transportation and advanced manufacturing.

The president also proposed "savings" of $850 billion over the next decade from the Iraq and Afghanistan military draw-downs. That earned criticism of a false promise since it is money that was never going to be spent.

Jacob Lew, the president's former budget chief and now his chief of staff, rejected that claim, however, saying that without "closing down this back door," there would be "a natural process of seeing military spending grow."

"I guarantee you that if we don't take the action that's been proposed, there will be leakage, and that money will end up being spent," he told "Fox News Sunday." "If there's going to be discipline in the budget, you have to lower the amount of money that could be appropriated in that area."

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