Question

If Vietnam fell to communism, what consequences did U.S. leaders think would result?

Answer 1

That neighboring countries would also fall into communism ( The Domino Effect ) 

Answer 2

The Vietnam War happened in the context of the Cold War, where the US and the USSR fought for world hegemony by implanting their economic models, capitalism and socialism respectively.

In this polarized world scenario, the US tried to prevent the Vietnam becoming another socialist country, which would strengthen the USSR and its regime.