Cuban Missile Crisis.
We had known for a bit of time that nuclear weapons had the capability of wiping humanity of the face of the earth with them but we had never come close to using them against another nuclear capable country. However people wouldn't want nuclear missiles in a country right next door capable of striking the country giving only minutes of warning.
After a U-2 surveillance plane found evidence of missile sights being setup on Cuba JFK takes the course of action to setup a blockade around Cuba and send back any ship carrying offense weaponry. The missiles if setup in Cuba could strike anywhere in the US except for Seattle. So to get the missiles removed the blockade or "quarantine" as it was called to be setup to prevent any more missiles. After talk the Russians removed the missiles from Cuba in exchange that the US removed them from Turkey however the missiles would be removed from turkey in at least six months while the missiles in Cuba would be removed immediately. Because the public did not know about the missiles being removed from Turkey the American public saw it as a great victory over the Soviets and that they were afraid.