WASHINGTON — Declaring the American dream under siege, President Barack Obama called Tuesday night for a flurry of help for a hurting middle class and higher taxes on millionaires, delivering a State of the Union address filled with re-election themes. Restoring a fair shot for all, Obama said, is “the defining issue of our time.”

Obama outlined a vastly different vision for fixing the country than the one pressed by the Republicans challenging him in Congress and fighting to take his job in the November elections. He pleaded for an active government that ensures economic fairness for everyone, as his opponents demand that the government back off and let the free market rule.

Obama offered steps to help students afford college, a plan for more struggling homeowners to refinance their homes and tax cuts for manufacturers. He threw in some politically appealing references to accountability,

including warning universities they will lose federal aid if they don’t stop tuition from soaring.

Standing in front of a divided Congress, with bleak hope this election year for much of his legislative agenda, Obama spoke with voters in mind.

“We can either settle for a country where a shrinking number of people do really well, while a growing number of Americans barely get by,” Obama said. “Or we can restore an economy where everyone gets a fair shot, everyone does their fair share, and everyone plays by the same set of rules.”

A rare wave of unity splashed over the House chamber at the start. Rep. Gabrielle Giffords, survivor of an assassination attempt one year ago, received sustained applause from her peers and hugs from many. Obama, too, embraced her as he made his way to the front.

Lawmakers leapt to their feet when Obama said near the start of his speech that terrorist leader Osama bin Laden, killed by a raid authorized by the president, will no longer threaten America.

At the core of Obama’s address was the improving but deeply wounded economy — the matter still driving Americans’ anxiety and the one likely to determine the next presidency.

“The state of our union is getting stronger,” Obama said, calibrating his words as millions remain unemployed. Implicit in his declaration that the American dream is “within our reach” was the recognition that, after three years of an Obama presidency, the country is not there yet.

He spoke of restoring basic goals: owning a home, earning enough to raise a family, putting a little money away for retirement.

“We can do this,” Obama said. “I know we can.”

In a signature swipe at the nation’s growing income gap, Obama called for a new minimum tax rate of at least 30 percent on anyone making over $1 million. Many millionaires — including one of his chief rivals, Republican Mitt Romney — pay a rate less than that because they get most of their income from investments, which are taxed at a lower rate.

“Now you can call this class warfare all you want,” Obama said, responding to a frequent criticism from the GOP presidential field. “But asking a billionaire to pay at least as much as his secretary in taxes? Most Americans would call that common sense.”

Obama calls this the “Buffett rule,” named for billionaire Warren Buffett, who has said it’s unfair that his secretary pays a higher tax rate than he does. Emphasizing the point, Buffett’s secretary, Debbie Bosanek, attended the address in first lady Michelle Obama’s box.

Obama underlined every proposal with the idea that hard work and responsibility still count. He was targeting independent voters who helped seal his election in 2008 and the frustrated masses in a nation pessimistic about its course.