Both President Johnson and President Kennedy held an assumption about the Vietnam War in common. They both assumed and expected that they could win the war. They both assumed that this could be accomplished militarily. They believed that the military could defeat the Vietcong insurgency thoroughly enough that people would stop supporting the insurgency to any serious degree. The people would then support the South Vietnamese government wholeheartedly and the war would be effectively over.
Of course, these assumptions turned out to be sadly mistaken. It is not at all clear if the two presidents were simply naïve or if the goals could have been accomplished. As it turned out, the war was not winnable. Neither the South Vietnamese forces nor the massive American presence that came about during Johnson’s time in office were capable of defeating the insurgency. This may have been due in large part to the inherent weakness of the South Vietnamese government. That government started out with less legitimacy than that of Ho Chi Minh in the North and it never caught up. The government was badly inept at trying to win the support of the people it claimed to govern.
Thus, both President Johnson and President Kennedy held an assumption/expectation that could not be realized.