From what I've read, when Kennedy discovered that the CIA had assassinated the South Vietnam President Ngô Đình Diệm, and his brother on November 2nd, 1963, he was planning on pulling what military was there, out of Vietnam. Kennedy was killed 20 days later. Kennedy hadn't wanted Diem dead as he felt that with Diem being a devout Catholic, and well liked, he would be a useful asset in relations with the Catholic population of South Vietnam.
As Bobby pointed out JFK was not going to withdraw and like so much about JFK such as the 1965 Immigration Act, the left has always moved the JFK controversies onto LBJ.
LBJ was terrible but if people start running dates and goals and political activities they will see that LBJ was largely completing JFK’s goals.