In an interview in late December with American Urban Radio Networks, a group of black-owned stations, Mr. Obama conceded that there was “grumbling” among African-Americans, especially about his jobs policies. But he rejected the idea that he should pay special attention to them  an argument that Earl Ofari Hutchinson, a black author and political analyst, called “disingenuous at best, and an insult at worst.”

Mr. Obama framed it this way: “I can’t pass laws that say I’m just helping black folks. I’m the president of the United States. What I can do is make sure that I am passing laws that help all people, particularly those who are most vulnerable and most in need. That in turn is going to help lift up the African-American community.”

Until now, black leaders have tended to tread lightly in criticizing Mr. Obama, and some find it painful. Black Americans remain overwhelmingly supportive of Mr. Obama; a recent ABC News poll found that 96 percent approve of his job performance.

But Elinor Tatum, the editor and publisher of the black-owned Amsterdam News, says that if blacks were asked “Is he doing a good job for African-Americans?” his numbers would be lower.

Image President Obama delivered remarks on Rev. Dr. Martin Luther King Jr. during services at the Vermont Avenue Baptist Church in Washington last month. Credit... Luke Sharrett/The New York Times

“Every time someone brings up an issue that affects blacks, he says that’s an issue that affects all of America,” Ms. Tatum said. “But at the same time, if he were of a different race or ethnicity, he would be playing to the black community. So there’s a double standard there. Should we be the victims in that?”

The conventional wisdom about Mr. Obama is that he tries to duck the issue of race, but close advisers say he is acutely aware of his role as the first African-American president and is trying to heighten racial sensitivity in constructive ways.