How can government get rid of poverty? It’s a question that gets asked not in a society where almost everyone is poor but in one giddy with surging growth and concerned about those who seem left behind—a society whose leaders have “an almost mystical belief in the infinite potentials of American society.”

Those are the words of Paul Jacobs, a prominent left-wing journalist and activist a half-century ago, quoted by Amity Shlaes in “Great Society: A New History.” Just as she presented a skeptical alternative to New Deal historians’...