"Harrison Bergeron" satirizes several types of societies or governments. First, it obviously mimics the dominating control of a totalitarian regime, where citizens have no rights, and the government sees and controls all. The H-G men coming to take young Harrison away from his parents without any resistance on their part is a good example of this. Moreover, The General Handicapper's execution of Harrison at the story's end is similar to Stalin's mass execution or imprisonment of anyone who dared to oppose him.
Vonnegut, like he does in many of his stories, also mocks some aspects of American society, not so much its government, but more so the conformity that is encouraged in American society through mass marketing/communication. George and Hazel's watching the TV constantly illustrates this criticism on Vonnegut's part. The author tries to warn Americans that some technology or messages from large corporations or the government strive to "equalize" America. Ironically, since the story was first published, America has actually become closer to the society portrayed in "H.B." A constant effort to make everyone equal with no winners or losers, to encourage people to dress alike by following the latest trends, or to buy the same items as everyone else is common in American culture.