To an extent, yes.
Step-by-step explanation:
The United States has been known for trying to stop the spread of communism or quarantine it. Many smaller countries can not fend off bigger countries and would just get engulfed in communism if outside forces like the United States did not help. Smaller countries would not stand a chance against countries like the communist Soviet Union or China during the Cold War.
So yes, since the United States has the power and number to help smaller countries and prevent the spread of communism, it is their responsibility to an extent. We can see this in the Truman Doctrine, which states that the United States would help smaller countries if they are being threatened by authoritarian forces.