Pres. John F. Kennedy's major response to the problems in Vietnam was to support the South Vietnamese government. Later in his presidency, he would allow Ngo Dinh Diem to be overthrown, but the basic idea remained the same. The US would, under JFK, support the government of South Vietnam to prevent it from being defeated by the communist insurgency.
JFK believed strongly in the idea of the domino theory. He believed that defending South Vietnam was vital to containing communism in general. This can be seen in the following quote from the link below. JFK, it says,
...feared that the loss of Vietnam to the Communists would trigger a wave of Communist aggression across the globe. "No other challenge is more deserving of our every effort and energy [than Vietnam]," he said. Kennedy added that if South Vietnam was lost to the Communists, "our [nation's] security may be lost piece by piece, country by country."
Because he believed in this, JFK pushed for the US to support South Vietnam. Over the course of his presidency, this support increased and more and more US troops were sent to Vietnam.