He cited statistics putting the gap between the rich and everyone else in the United States on a par with that in Jamaica and Argentina, and showing that children have a greater chance in Canada, Germany or France to move up the social ladder than they do in the United States. The trend, he said, was bad for the economy, social harmony and democracy.

Describing what steps he has taken, Mr. Obama highlighted the health care law.

For decades, he said, health care “was one yawning gap in the safety net that did more than anything else to expose working families” to economic insecurity. “That’s why we fought for the Affordable Care Act,” he said.

Despite the program’s problems, he added, the number of insured people is up, medical costs are down and all Americans with insurance have new protections and benefits.

“It is these numbers, not the ones in any poll, that will ultimately determine the fate of this law,” Mr. Obama said, adding, “This law is going to work, and for the sake of our economic security, it needs to work.”

Among Republicans seeking the law’s repeal, Mr. Obama singled out Senator Mitch McConnell of Kentucky, the minority leader, whose state has one of the most successful new insurance marketplaces: “He might want to check with the more than 60,000 people in his home state who are already set to finally have health insurance.”

Still, prospects for Mr. Obama’s goals in his final three years are hardly promising. His speech came at the close of a year in which none of his other economic initiatives have made it through Congress.

The Senate passed a bipartisan, business-backed immigration bill to give about 11 million illegal immigrants a path to citizenship, but House Republican leaders refuse to take it up. Budget talks with Senate Republicans fizzled, probably dashing Mr. Obama’s three-year-old hopes of a “grand bargain” on spending and taxes, one that would combine deficit reductions in future years with immediate financing for infrastructure, education and technology projects. Spending cuts are squeezing the very programs that Mr. Obama has wanted to expand.