I was quite small, but I remember it fairly well. Dad was a sergeant in the USAF Strategic Air Command; he had to go back in to work, and lived on-base for several days. My mom was freaked out, as were her friends who visited.
Later history is all about Oswald the Lone Assassin, but at the time everyone thought it was the the beginning of World War III, and most of the Northern Hemisphere was going to become a radioactive wasteland.