WASHINGTON - President Barack Obama’s proposed federal budget would shrink annual deficits over 10 years, but would fall far short of taming the nation’s exploding federal debt.

By the end his second term, if he’s re-elected, debt held by the public would rise to $15.7 trillion. That’s more than double the $7.5 trillion national debt he inherited when he came into office. And debt held by the public is projected to keep rising under his budget, reaching $19.5 trillion by 2022.

Meanwhile, Obama’s budget wouldn’t slash annual budget deficits, but would reduce them to levels seen as less threatening _ but still high.

After spending 2011 fighting with Congress over how to cut the budget, Obama projects

that the fiscal 2012 deficit actually will rise, to $1.326 trillion -slightly higher than last year’s $1,299 trillion.

Annual deficits then would shrink, to $612 billion in fiscal 2017 - which starts Oct. 1, 2016, the final year of Obama’s second term if he wins re-election. While that’s a sizeable drop, $612 billion still would be higher than any deficit ever recorded before Obama took power - nominally, though not as a share of the economy.

Annual deficits would creep back up through fiscal 2022, but as a percentage of gross domestic product - the value of all U.S. goods and services produced in one year - the deficit would fall from 8.5 percent in fiscal 2012 to 3 percent in fiscal 2017, a level most economists say is sustainable.

To get that, Obama would raise taxes on the wealthy. He’d let Bush-era tax cuts expire for American families with taxable income above $250,000, and for single filers over $200,000. He’d end preferential treatment of dividends from stocks; they’d be taxed as ordinary income for those in higher brackets. He’d limit their itemized deductions, roll back their personal exemptions and raise the tax rate on their capital gains - profits from sale of stocks, bonds, real estate and the like - up to 20 percent from 15 percent now.

Those tax hikes have no chance of passing the current Congress, owing to Republican opposition. With them Obama is showing voters his preference for how to attack deficits.

Republicans have called for sharper spending cuts and substantial overhauls for Medicare and Medicaid, whose long-term financial shortfalls are prime drivers of future deficits.

On Election Day Nov. 6, Americans will choose between two clearly competing visions of federal government and federal finance.

Former Comptroller General David Walker, appointed by President Bill Clinton as the nation’s chief auditor, sharply criticized Obama’s budget.

"The proposed budget would greatly increase the portion of government spending that is on ‘auto-pilot.’ While the president’s budget cuts discretionary spending programs by 1 percent over a 10-year period, mandatory spending programs and interest on debt grow by more than 96 percent over the same decade," Walker said. "The result is that in the year 2022 more than 78 percent of total outlays (spending) will be on auto-pilot-which is both irresponsible and unsustainable."

At the end of a second Obama term, federal spending would amount to about 22.2 percent of GDP. That’s about one point above historical averages. Incoming revenues would amount to about 19.2 percent of GDP, also about one point higher than historical averages.