What did American leaders think was at stake in places like Korea, Berlin, and Cuba?
What American leaders thought was at stake in all of these places was nothing less than control of the world and the survival of freedom. They believed that each confrontation with communism was part of a larger clash in which control of the world was at stake. They did not believe that losing in any one of these places would by itself lead to the defeat of capitalism and democracy, but they felt that any loss would be a step towards that outcome.
In all of these places, the US was trying to contain communism. This was the major American goal in the Cold War. American leaders wanted to prevent communism from spreading because they felt that the Soviets were trying to take over the world. Therefore, they felt that each conflict (whether in Korea, Berlin, or Cuba) was a test of American resolve. They felt that control of the world and the survival of freedom was at stake in each confrontation.