John F. Kennedy, Oval Office, 1962

“Are we going to give up in South Vietnam?” That was the question President Kennedy posed, then tried to answer, in what would be his final news conference in 1963. “The most important program, of course, is our national security. But I don’t want the United States to have to put troops there.” Kennedy was killed eight days later, giving rise not just to 40 years of grassy-knoll conspiracy theories but also to a lingering debate over whether he might have averted his successor’s tragic plunge into the jungles of Southeast Asia. Kennedy came to public life as a staunch anti-Communist, but his experiences as president — most notably...