RFK declared the war "won" when we agreed to a peace that pushed the division of the Vietnams to the 13th parallel north in his first term. We then proceeded to arm the South Vietnamese to the teeth even further.
JFK was the one under whom the war started, not LBJ, and he was the one who ultimately pulled the plug after he won "Bobby's third term" in 1976 as the South Vietnamese Government proved too inept to defend itself.