There are two scenarios which I'll briefly outline:
A) Ho accepts LBJ's Manila offer of 1966, which means phased withdrawal, and since SVN is undergoing a political transition between the Thieu-Ky junta to the semi-parliamentary one of OTL in 66-67, and without military benefits of Vietnamization or proper equipment, expect Saigon to fall by 1970 latest. Results: LBJ gets re-elected. If Nixon's smart he waits until 1972, otherwise he's finished for good. Now for 1972, there are two scenarios...
A1) HHH gets the nomination, and loses to Nixon or perhaps even Reagan. Nixon's presidency goes similar to OTL, probably without Watergate. RFK-Reagan in 1980. Depending on how Nixon performs with the economy, I'd say narrow RFK win and blowout in '84. I've outlined an RFK Presidency before.
A2) RFK gets the nomination and wins against Nixon. Nixon is finished, the war is lost already, and we see a domestic focus with detente to the USSR, perhaps PRC as well.
B) LBJ fights the war properly, resulting in an increased antiwar movement. Tet is successfully portrayed as the major military victory it was. Using the toolkit of incumbency, HHH wins the '68 nomination, losing to Nixon, where Watergate is covered up successfully (no tape on the door and bugs work) and either RFK-Connally or RFK-Reagan in '76.