You just nailed it.
It's interesting, really. The youth of the '60s were perfectly positioned to be susceptible to the propaganda they recieved from the socialists.
-They were used to an easy life compared to their fathers;
-They grew up believing that it was their DUE;
-The thought of having to give up their easy lives for the risk-filled and hard life of the military, even for only a few years, terrified them;
-They were the first generation of Americans to widely go to higher education;
-They were, in college, separated from their parents and families' influence;
-They were at a moment in their lives when they were looking for "something to believe in";
-Because of the above, they were particularly susceptible to socialist guilt-trips;
-Their professors and the Soviet-influenced radicals could, therefore, easily supplant their parents, at a crucial moment in their lives;
-The radicals made themselves "cool" and "stylish", thus increasing the lure.
All in all, it was the perfect time for the Communists to strike. The payoff for them can still be seen...it actually outlived the Soviet Union itself, and the discreditation of communism around the world.