The story explains that the handicap laws are put into place to ensure complete and perfect "equality." Instead of this being the equality of opportunity that founded the U.S., the laws ensure equality of outcome; nobody is allowed to excel, and so everyone ends up at the same place in life and in society. There are no specialized jobs; instead, people who are completely unqualified are encouraged to perform above their ability, such as the stuttering news announcer, while people with exceptional skills are handicapped so nobody will feel inferior.
The year was 2081, and everybody was finally equal. They weren't only equal before God and the law. They were equal every which way. Nobody was smarter than anybody else. Nobody was better looking than anybody else. Nobody was stronger or quicker than anybody else. All this equality was due to the 211th, 212th, and 213th Amendments to the Constitution...
(Vonnegut, "Harrison Bergeron," tnellen.com)
The people do not rebel for two main reasons. First, it is understood that this outcome was due to public insistence; the public demanded that everybody be treated equally, but also insisted that no one suffer consequences, or be treated differently for their abilities or lack thereof. The response to this was not to raise the undereducated or under-abled, but to lower the educated and over-abled to the average level. Secondly, after the handicap laws are put into place, the people are prevented from thinking about their position through the handicaps themselves; this is shown by George, who is intelligent enough to know that the laws are immoral, but is prevented from thinking by his mental handicap.