Straddling the line between governance and politics, Mr. Obama told wealthy contributors at a Democratic fund-raiser here that their party was not the only one that cared about the troubles of the country, and he renewed his commitment to bipartisanship despite the divisions in Washington.

“Occasionally I may make some of you angry because I’m going to reach out to Republicans, and I’m going to keep on doing it,” he said. “Even if some of you think I’m a sap, I’m going to keep on doing it because that’s what I think the country needs.”

He went on to say he still would prefer a Democratic-controlled Congress, because when his party can set the agenda, “we don’t have a country where just a few are doing really well.”