Joe Biden can be heard on the Nixon tapes. President Nixon called Mr. Biden on Tuesday, Dec. 19, 1972. The president had returned from Camp David, where he had been planning an ambitious second-term government reorganization. Delaware’s Sen.-elect Biden had narrowly defeated a popular incumbent and Nixon ally, Caleb Boggs, 13 days before his 30th birthday. He became the second-youngest person ever elected to the Senate. Nixon—who won Delaware by more than 20 points in his 49-state landslide—took note of this rising star, who had flipped a GOP Senate seat. “If I had gone to Delaware, it wouldn’t have changed...