What were the sources of Senator Joseph McCarthy's popularity? What brought about his downfall?

Joseph McCarthy became popular because many Americans
(especially conservatives) were very suspicious of communists and thought that
communists were likely to try to take over the US from within.  Because McCarthy seemed
to be a regular guy who was fighting elites who were probably communists, he was quite
popular.  This was especially true at first when the Korean War and the "fall" of China
were still fresh in people's minds.

McCarthy fell largely
because he overreached.  He started to claim that people within the army were
communists.  When he did this, he ran up against a part of the government that most
people respected.  So now, instead of attacking egg headed elites, he was attacking
respected military people.