Welll..... you're being pretty liberal with reality.
Vietnam happened over a long period of time. Eisenhower was in charge when the Vietnam War started to kick off. By 1960 the US had 900 troops in Vietnam already.
Yes, the largest increase happened in 1965 which was Johnson.
The reality is that the Korean War, the Vietnam War etc were proxy wars in the Cold War. The Cold War was very much an "anti-Communist war" and the right did far, far more at pushing anti-Communism.
By the time Johnson came along, being "anti-Communist" had almost become essential in the US because of what the right had done.
At the same time, I wasn't necessarily talking presidents. I was talking support among the people. The right supported the Vietnam War far more than the left. Democratic presidents need to get support from the right, Republicans from the left, in order to win elections.