In the 1968 election, there was very little support for the Vietnam War from the major candidates for the presidency. By the time the election was in full swing, the Tet Offensive had helped to turn Americans fairly decisively against the war. It was the public reaction to the Tet Offensive that caused President Johnson to choose not to run again. In other words, the Vietnam War was fairly toxic by this point.
Even so, the Democratic nominee, Hubert Humphrey, campaigned on a platform that supported the war and supported Johnson’s policies. This was not surprising since Humphrey had been Johnson’s vice president and would have had a very hard time remaining credible while running against the war. Humphrey defeated Eugene McCarthy, who was very strongly in favor of pulling out of Vietnam. We will never know what would have happened if Robert F. Kennedy, who was also in favor of withdrawal, had not been assassinated.
Humphrey then ran against Richard Nixon in the general election. Nixon promised that he would be able to end the war without a humiliating defeat. However, he never said exactly how he would do this. This made political sense for him. Humphrey was tied to Johnson’s unpopular policy and it made sense for Nixon to simply declare that he would do something different without attracting criticism by detailing his plans.
Thus, the election pitted a defender of the status quo against a candidate who simply said that he would end the war but did not say how he would accomplish this feat.