The most important impact of the Vietnam War on this election was that it forced Pres. Lyndon B. Johnson to not run for reelection.
Perhaps the second most important impact of the War was that that it led to the nomination of Hubert Humphrey and to a lack of support for him among many Democrats.
Finally, I would argue that the War helped to get Richard Nixon elected. This was because the "Silent Majority" got tired of all the protests and things like that and went for Nixon since he was more of a "law and order" candidate.
As with the previous post, check a textbook or class reference for an answer to this. I would say that the Vietnam War impacted the election hopes of President Johnson in 1968, as he decided not to run again for the office of President, convinced that he would not win reelection from his own party. The issue of Vietnam, at this point, injected other people into the discussion of Presidential aspirations. I would indicate that the Vietnam War significantly affected the candidacies of Eugene McCarthy, who posted a sizeable showing in the New Hampshire Primary, convincing President Johnson to not seek reelection. It also allowed Senator Robert Kennedy to enter the political fray, appealing to the youth vote in that he was going to end the conflict in Vietnam. Finally, the Vietnam War impacted the election of President Nixon in 1968 because, with the death of Kennedy via assassination, and the belief that the Democrats could not navigate their way through a convention, not to mention the Vietnam War, Americans became convinced that a Republican like Nixon was needed to ensure that America could reassert its rightful place in the world with a sense of dignity and with the belief that peace can be sought, but "not at any price."
President Lyndon Johnson decided not to run for a second term in part because of the unpopularity of the Vietnam War. Robert Kennedy seemed like a likely successor before he was assassinated, and following his death, the Democratic party was splintered. Hubert Humphrey got the nomination, but anti-war candidate Eugene McCarthy galvanized many youthful supporters. George Wallace even broke away from the party and ran as an independent. Violent protests interrupted the Democratic National Convention in Chicago, particularly by members of the Yippies and SDS (Students for a Democratic Society).