When President Obama greets African-Americans who broke barriers, he almost invariably uses the same line.

“I wouldn’t be here if it weren’t for you,” he said to Ruby Bridges Hall, who was the first black child to integrate an elementary school in the South. The president repeated the message to a group of Tuskegee airmen, the first black aviators in the United States military; the Memphis sanitation workers the Rev. Dr. Martin Luther King Jr. addressed in his final speech; and others who came to pay tribute to Mr. Obama and found him saluting them instead.

The line is gracious, but brief and guarded. Mr. Obama rarely dwells on race with his visitors or nearly anyone else. In interviews with dozens of black advisers, friends, donors and allies, few said they had ever heard Mr. Obama muse on the experience of being the first black president of the United States, a role in which every day he renders what was once extraordinary almost ordinary.

But his seeming ease belies the anxiety and emotion that advisers say he brings to his historic position: pride in what he has accomplished, determination to acquit himself well and intense frustration. Mr. Obama is balancing two deeply held impulses: a belief in universal politics not based on race and an embrace of black life and its challenges.