Read the passage: But to fail to ask of him—and of all Americans—perseverance within the processes of a free and responsible society would be to fail to ask what the national interest requires of all its citizens. What is Johnson arguing in this passage?
He's asking white Americans to fight harder on behalf of the Negro.
He's pointing out that the fight for equal rights is the work of all citizens of a free society.
He's accusing white Americans of not asking the right questions.
He's saying that white Americans should encourage the Negro to fight harder.