“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.

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.

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.”