WASHINGTON (AP) — President Barack Obama took a significant step toward retooling his presidency with a challenge to lawmakers to rise above partisan differences to tackle economic and budget problems "decades in the making."

And while there remained stark differences in approach between the president and the Republicans with whom he now shares power, Obama made some striking concessions in the name of national unity — and asked others to do the same.

In a State of the Union address made somber by the recent Arizona shootings, Obama on Tuesday night coupled a call for budget restraint with a plea for more American innovation to allow the United States to better compete in the global economy.

"The rules have changed" and the U.S. must not let itself be left behind by other fast-growing economies like China and India, Obama said.

Obama and newly empowered Republicans each framed their rival political themes, ones that will carry them to the 2012 elections.

Obama's speech was relatively subdued. "He avoided competing with his audience," said Wayne Fields, a professor at Washington University in St. Louis who studies presidential rhetoric. "They seemed as much a part of the show as he was. The message from both sides was that we're going to work together in a civil society."

With signs that the recovery is beginning to pick up steam, the occasion gave both parties a chance to look forward — not back to the economic mess in the nation's rear-view mirror.

"Now that the worst of the recession is over, we have to confront the fact that our government spends more than it takes in," Obama told a House chamber filled with many new House and Senate faces, mostly Republican ones.

Obama's wish list included new government "investments" in education and infrastructure such as roads and bridges and more market-opening deals with other nations.

He called for more spending on high-speed rail and high-speed Internet. And in a key concession, one that quickly riled environmentalists, Obama called for spending on clean-energy technology — but for the first time included nuclear power, "clean" coal and natural gas.

While praising a call by Obama to end oil subsidies, League of Conservation President Gene Karpinski said, "We object to his attempt to redefine clean energy to include nuclear and so-called 'clean coal.'"

"At stake is whether new jobs and industries take root in this country, or somewhere else," Obama said. "To win the future, we'll need to take on challenges that have been decades in the making."

At the same time, Obama proposed deficit-cutting steps, including a five-year freeze in spending for some domestic programs. And he called for a reduction in the taxes corporations pay but "without raising the deficit."

Republicans scoffed at Obama's concept of "investments" and suggested the president was merely seeking to continue a longtime spending spree. They've put tackling the nation's $14 trillion debt at the center of their agenda, beginning with spending cuts larger and sooner than Obama has proposed.

It's a goal that resonates with tea party factions within the GOP. Republicans assert that taming soaring deficits, not adding to the debt, will put the economy back on the path of growth and spur private-sector job growth.

Earlier Tuesday, the Republican-controlled House voted 256-165 to return most domestic agencies to 2008 budget levels, a largely symbolic vote.

Obama agrees that tackling trillion-dollar-plus annual deficits is a national priority — but a long-range one, not one that needs to be taken on too aggressively with the unemployment rate stubbornly stuck above 9 percent.

But even the House GOP effort at fiscal austerity would only make a small dent in the nation's debt.

"Americans are skeptical of both political parties, and that skepticism is justified — especially when it comes to spending," said House Budget Committee Chairman Paul Ryan, R-Wis., in a prepared text for the GOP response. "So hold us all accountable."

And, trying to strike the same tone of congeniality that Obama used, Ryan praised the president for focusing on the economy and deficits. "He was right to do so, and some of his words were reassuring."

As they laid out their positions, the risks were high for both parties.

Obama needs to win back independent voters, who helped him win the presidency in 2008 but deserted Democratic candidates in favor of Republicans in last November's midterm elections.

Despite their new clout, Republicans, too, are mindful that repeating the gains they made last November in the 2012 election cycle won't be a cakewalk — and need to avoid the possibility of gridlock.

"Everybody, not just Obama but members of Congress, want to have something to show for the next two years," said Rutgers political science professor Ross Baker.

For the first time in a while, Obama has some wind at his back, something Republicans hadn't counted on just a few months back. His State of the Union address followed a moving speech after the Tucson shootings and a well-executed summit and state dinner with President Hu Jintao of China.

Ever since what he called his party's "shellacking" in the midterm elections, Obama has moved to mend fences with business and move toward the center. He extended existing Bush-era tax cuts, introduced new ones, completed a free-trade agreement with South Korea, and ordered a government-wide review of regulations with a goal of weeding out ones that hinder business.

For the first time, Obama vowed Tuesday night to veto any bills sent to him that include "earmarks," pet spending provisions pushed by individual lawmakers. It was a turnabout for the president, who in 2009 said earmarks were fine if "done right."

But it wasn't all concessions. Obama strongly defended his health care overhaul from GOP efforts to dismantle it.

In all his recent dealings, Obama "had to bow to practical realities," said Thomas Mann, a senior fellow at the Brookings Institution. "What he is contesting," Mann adds, "is the Republican characterization of him as this out-of-control liberal."