In part, the Vietnam War was perceived as a message that the U.S. would not be intimidated by a Chinese nuclear-weapons program.
You've probably heard that, as Jeremi Suri reported in Wired five years ago, after the Paris Vietnam peace talks broke down in 1969…
Frustrated, Nixon decided to try something new: threaten the Soviet Union with a massive nuclear strike and make its leaders think he was crazy enough to go through with it. His hope was that the Soviets would be so frightened of events spinning out of control that they would strong-arm Hanoi, telling the North Vietnamese to start making concessions at the negotiating table or risk losing Soviet military support.
Codenamed Giant Lance, Nixon's plan was the culmination of a strategy of premeditated madness he had developed with national security adviser Henry Kissinger. … Giant Lance was the leading example of what historians came to call the "madman theory": Nixon's notion that faked, finger-on-the-button rage could bring the Soviets to heel.
Nixon and Kissinger put the plan in motion on October 10 … They wanted the most powerful thermonuclear weapons in the US arsenal readied for immediate use against the Soviet Union. … After their launch, [B-52s armed with nuclear weapons] pressed against Soviet airspace for three days. They skirted enemy territory, challenging defenses and taunting Soviet aircraft. [The strategy] appeared to be a direct application of … game theory. H. R. Haldeman, Nixon's chief of staff, wrote in his diary that Kissinger believed evidence of US irrationality would "jar the Soviets and North Vietnam." Nixon encouraged Kissinger to expand this approach. "If the Vietnam thing is raised" in conversations with Moscow, Nixon advised, Kissinger should "shake his head and say, 'I am sorry, Mr. Ambassador, but [the president] is out of control." Nixon told Haldeman: "I want the North Vietnamese to believe that I've reached the point that I might do anything to stop the war. We'll just slip the word to them that for God's sake, you know Nixon is obsessed about Communism. We can't restrain him when he is angry — and he has his hand on the nuclear button' — and Ho Chi Minh himself will be in Paris in two days begging for peace."
Whether it helped end the war, but the U.S.S.R. bought Nixon's act. Suri again:
Brezhnev's ambassador to the US, Anatoly Dobrynin, urgently set up a meeting with Nixon and Kissinger. … Dobrynin warned Soviet leaders that "Nixon is unable to control himself even in a conversation with a foreign ambassador." He also commented on the president's "growing emotionalism" and "lack of balance."… On October 30, Nixon and Kissinger ordered an end to Giant Lance, and the B-52s turned and headed back home. The sudden conclusion reinforced the madman pose.
Hmm, one would have thought the Soviets already knew Nixon was crazy. Anyway, the Vietnam War was a test case for yet another element of U.S. nuclear-weapons policy. I'm currently reading Francis J. Gavin's illuminating Nuclear Statecraft: History and Strategy in America's Atomic Age by (Cornell University Press, 1912). He writes (emphasis added):
The dilemmas associated with nuclear proliferation influenced US military strategy throughout the world, most obviously in Europe. But a linkage also existed between a more active nonproliferation policy and the US military presence in Southeast Asia. The Gilpatric committee discussions [which led to the nuclear Non-proliferation Treaty] took place when the Johnson administration was debating whether to escalate US military involvement in Vietnam. China's atomic test was bound to influence these discussions. President Kennedy had considered a nuclear-armed China a grave threat that would "so upset the world political scene [that] it would be intolerable." Convinced that China was "bound to get nuclear weapons, in time, and from that moment they will dominate South East Asia," Kennedy feared that even a minimal Chinese nuclear force could prevent US military intervention. As Kennedy had once noted, just a few missiles in Cuba had "had a deterrent effect on us."
President Kennedy's analysis implied that once China acquired a nuclear capability, the United States would likely withdraw from Vietnam.… But government officials, as well as members of the committee, wanted to make clear that the United States would not break its commitments in the face of a nuclear threat. If the United States acquiesced to a nuclear-armed adversary, the incentives for small powers to develop nuclear weapons would increase exponentially. Vietnam would be the test case of this new commitment. In a paper for the Gilpatric committee, the deputy assistant secretary of defense for international security affairs Henry Rowen wrote, "A U.S. defeat in Southeast Asia may come to be attributed in part to the unwillingness of the U.S. to take on North Vietnam supported by a China that now has the bomb. Such a defeat is now much more significant to countries near China than it was before October 16."