Explanation
President Kennedy was speaking in broad terms of the Cold War struggle against Soviet expansion. We can assume he wanted Americans to support this struggle in some way. Fighting in the military, joining the Peace Corps, and paying taxes, would all be ways of supporting this struggle, but Kennedy wasn’t just thinking of one of these things in particular, and the question specifically asks for the “broad” goal. Kennedy supported the civil rights movement), but he was not talking about that in this part of his speech.