Deporting a person for his beliefs and ideologies seems like the opposite of American fundemental rights such as freedom of speech, how come the Justice Department ignored Americans basic rights? What caused so widespread fear that McCarthy could point fingers at whoever he choosed? Even the president?
As stated the question is a bit leading. However to answer it I would recommend looking at a few things.
Labor unions and Socialists where making headway with popular opinion during the early 1900's. There where unions created across vast number of trades. Also Eugene v. Debs got almost a million votes for the president. There where also Dozens of Mayors elected as pure Socialists.
However with socialism came an off shoot. That was Anarchism. This off shoot led to something called the Palmer Raids.
The Palmer Raids came about because Anarchists set off Dozens of bombs and send hundreds of mailbombs to government officials and prominent men including the Attorney General, several congressmen and senators, and John D Rockefeller.
This culminated in the worst terrorist act in the NYC up until 9/11 and that was the Wall Street Bombing.
After that Palmer Raids happened. Though it was Anarchists that did it it Socialists and Communists where lumped in as well due to being of like mind (Both wanting to destabilize Capitalism) and more importantly of convenience in getting rid of agitators.
So we see how in small part ( as with everything it is always more complicated)the first scare happened.
With McCarthyism some of it had to do with Russians stealing the plans for the Atomic Bomb. The Rosenberg trial you should look at it.