During the sixties, Americans still lived in fear of a nuclear holocaust. It was during the early sixties that the Soviet Union placed offensive missiles in Cuba aimed at the United States, possibly the closest the world has come to nuclear war. It was also during the sixties that American involvement in Vietnam became intense as a result of an attempt to stop the spread of communism. Americans were regaled with advertisements depicting Nikita Khruschev, the Soviet Premier, stating "we will bury you." Although the McCarthy hearings had ended with some degree of embarrassment for Americans, there was still a great deal of superstition about anyone who disagreed with government policy. When John F. Kennedy was assassinated, great mention was made of the fact that Lee Harvey Oswald had spent time in the Soviet Union and had attempted to renounce his American citizenship. So there was still a great deal of fear bordering on paranoia.
This is a very difficult question to answer because it is so vague. There are many ways that the question could be answered.
One way to look at this is to say that the conditions were frightening. The 1960s were a decade in which the Cold War was relatively "hot." The Cuban Missile Crisis, in particular, made this a time when people were very afraid of the possibilty of an actual nuclear war. In addition, it was during this time that communism seemed to be advancing. The communists had taken Cuba at the end of the 1950s and were fighting against the US and its allies in Vietnam. This would have helped cause an atmosphere of fear in the US.
So, one way to describe the historical conditions at this time is to say that it was a time of great anxiety for the American people.