President Barack Obama rolled out a $3.78 trillion budget Wednesday, angering Republicans with a call for higher taxes on the rich while worrying liberals by countenancing cuts to retirement benefits.

Much was familiar in Obama's blueprint, rooted in his enduring campaign to shield the American middle class and to cut deficits without massive cuts in infrastructure, education spending and cherished social programs.

The plan effectively set Obama's battle lines ahead of a new fiscal showdown with Republicans, and was largely an academic exercise since it has no chance of being enacted in full in divided Washington.

"For years, the debate in this town has raged between reducing our deficits at all costs and making the investments necessary to grow our economy," Obama said on an unseasonably warm morning in the White House Rose Garden.

"This budget answers that argument, because we can do both. We can grow our economy, and shrink our deficits."

Republicans however immediately rejected Obama's plans. Senate Minority Leader Mitch McConnell branded them as a "left wing wish list."

House Speaker John Boehner, who has already passed a Republican budget that slashes spending, warned that Obama had already made life tough enough on the rich, adding: "We don't need to be raising taxes on the American people."

Somehow, the two sides, currently also at odds over gun reforms and tax policy, and fresh from bitter recent duels over fiscal policy, will have to broker a compromise to fund the budget for fiscal 2014.

The blueprint included one key concession to Republicans, which has already angered elements of Obama's liberal Democratic base.

Obama signaled he is ready to modify the inflation-linked formula by which some retirement benefits are calculated -- meaning that payments could diminish, causing consternation among some Democrats on Capitol Hill.

The move, ahead of a second dinner between Obama and Republican senators at the White House later Wednesday, was intended to try to lure some support ahead of cross-party budget and deficit talks.

Officials say Obama's plan includes $1.8 trillion of deficit reduction over 10 years and would raise $580 billion in new revenue by curbing income tax breaks for the rich, without raising rates.

Republicans dispute Obama's deficit reduction claims, arguing that since the budget would dispense with $1.2 trillion in automatic spending cuts, which began in March and are known as the sequester, its real deficit reduction figure would only be $600 billion in savings.

Republican House budget committee chairman Paul Ryan said he was disappointed with Obama's blueprint, but did give Obama some credit for being willing to address costs of social programs known as entitlements.

"At least he put something here that shows his willingness to address entitlements, and so that gives me a glimmer of hope that there is a way of getting to an agreement by the end of the day," Ryan said.

In other measures, Obama's budget would raise the tax on a pack of cigarettes from $1.01 to $1.95 per pack to finance early childhood education schemes.

It would also provide $1.65 billion for the Global Fund to Fight AIDS, Tuberculosis and Malaria and $4 billion to allow security upgrades following the attack on the US consulate in the Libyan city of Benghazi last September.

The Pentagon said the budget would hold military spending steady but would not account for the cost of the war in Afghanistan -- which is expected to surpass $80 billion in the current year.

The plan would also boost funding for major science, health and research programs and find room to sustain Obama's challenge to NASA to send humans to an asteroid in 2025 and to Mars in 2030.

Among fiscal measures opposed by Republicans, the Obama budget would implement the "Buffett Rule," which would mandate that households making more than $1 million a year pay at least 30 percent of income in taxes.

The budget foresees a deficit of $744 billion, or 4.4 percent of GDP, in 2014 -- down from a projected deficit of $973 billion this year.

Officials projected that the shortfall would reach 2.8 percent of GDP by 2016 and 1.7 percent by 2023.

The plan assumes unemployment will average 7.2 percent next year, down from the current 7.6 percent.

Economic growth meanwhile is predicted to pick up to 3.2 percent next year, from 2.3 percent this year.

The White House says that the plan represents more than two dollars in spending cuts for every one dollar of new revenue accrued from closing tax loopholes and would not add a dime to the deficit.