Overhauling the tax codes would be a priority in a second Obama term. Later this month, the administration will propose a revision of the corporate tax code to root out many tax breaks and lower the 35 percent rate, though Mr. Obama said the change must not raise any more revenues than the current system, despite the nation’s chronic deficits.

While many of his ideas are retreads of proposals Republicans and some Democrats have blocked before, for the first time Mr. Obama proposed to tax dividends like ordinary income for taxpayers who make more than $250,000, as dividends were before the Bush administration. The change, which would nearly double the rate for affluent taxpayers to 39.6 percent from 20 percent, would raise about $206 billion over 10 years.

Republicans are certain to oppose such tax increases as they have before. But the question this year is whether Mr. Obama after the election, win or lose, can use his veto and looming budget deadlines to force some compromises — even a “grand bargain” of spending cuts and revenue increases for deficit reduction could be possible, Mr. Obama has told people privately.

“The president’s budget is a reasonable opening move for what will likely be major budget negotiations after the election and before the Bush tax cuts are due to expire at the end of the year,” said Jim Kessler, vice president for policy at Third Way, a centrist policy organization.

“The real work begins in November, and right now these opening moves are just pawns shifting on the chessboard,” Mr. Kessler added. “As a deficit hawk, I’m guardedly optimistic about this budget.”

After the election, Republicans will be eager to forestall two legislative events. One is the expiration of the Bush-era tax cuts after Dec. 31; Mr. Obama in his budget reiterated his vow to support an extension only for taxpayers making less than $250,000. The second comes in January, when $1.2 trillion in automatic 10-year spending cuts begin, half in military programs, unless the White House and Congress agree to alternative savings.

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Republicans will need Mr. Obama’s signature to win legislation that alters either of those events.

The president’s budget incorporates his alternative to the automatic cuts. Mr. Obama claims $3 trillion in deficit reduction from higher revenues and spending cuts, on top of nearly $1 trillion in cuts over 10 years from annual discretionary spending that he and Congress agreed to in a deal last August. That does not include the so-called entitlement programs, Medicare , Medicaid and Social Security , whose fast-growing costs — especially for Medicare — are driving the projections of mounting federal debt.

The budget, with its trade-off of higher taxes on the wealthy for initiatives benefiting lower- and middle-income workers, reflects Mr. Obama’s campaign themes. Polls show that Americans by large majorities support taxing the wealthy more. And Democrats believe they have a potent issue in Republicans’ dogged opposition, especially if the Republican nominee turns out to be Mitt Romney , the former Massachusetts governor whose personal fortune and acknowledged relatively low tax rate for his investment and dividends income have had him on the defensive even in the Republican nomination contest.

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Mr. Obama traveled to Northern Virginia Community College near Washington to unveil his budget before a gymnasium packed with the sort of young voters his re-election campaign is courting. As he did in the State of the Union address last month, Mr. Obama framed the budget debate as an effort to make sure “everyone plays by the same set of rules, from Washington to Wall Street to Main Street.”

He rousingly promoted his initiatives to make college more affordable and to train workers for health care, the sciences and advanced manufacturing. And he called for Warren E. Buffett and other wealthy Americans to pay an income tax rate no lower than what secretaries pay. Mr. Obama’s “Buffett Rule” would set a minimum 30 percent rate on income above $1 million, replacing the current alternative minimum tax that increasingly hits upper-middle-class taxpayers.

“We don’t begrudge success in America,” Mr. Obama said. But, he added, “We do expect everybody to do their fair share, so that everybody has opportunity, not just some.”

At the Capitol, Senator Mitch McConnell , the Republican minority leader, said Mr. Obama “released a budget that isn’t really a budget at all. It’s a campaign document.”

He ridiculed Senate Democrats for saying they would not put the budget to a vote, though Republicans did not offer Bush administration budgets for a vote, either, given the likelihood of defeat. And Mr. McConnell chastised the White House chief of staff, Jacob J. Lew , who until recently was Mr. Obama’s budget director, for incorrectly saying on Sunday television talk shows that a budget needs 60 Senate votes to pass so Republicans would block it; a budget resolution needs a simple majority.

Republicans slammed Mr. Obama for breaking a promise at the start of his term to cut the deficit in half, measured as a share of the economy. Administration officials counter that few people knew in early 2009 how severe the recession was, and each year global forces like Europe’s debt crisis have stymied a full recovery.

The current year’s deficit of $1.3 trillion is the same in dollar terms as when Mr. Obama took office. Measured as a share of an improved economy it is smaller — 8.5 percent of the gross domestic product compared with 9.2 percent in 2009. For 2013 the deficit would be $901 billion, or 5.5 percent of G.D.P.