We learn in the opening to "Harrison Bergeron" that:
All this equality was due to the 211th, 212th, and 213th Amendments to the Constitution, and to the unceasing vigilance of agents of the United States Handicapper General.
As of 1961, when the story was published, the Constitution had only been amended 23 times—and only 13 since the 1790s. Therefore, Vonnegut, in envisioning 200 more amendments, is conveying to his readers that the Constitution has been radically altered by 2081. Two hundred amendments would almost certainly add more words total to the Constitution than were there to begin with, so we can imagine the Constitution is a completely redesigned document by this time.
We discover from the story that the original American notion of equality as equality of opportunity has been completely redefined. In this story, equality is understood as an absurd process of leveling everyone to the lowest common denominator so that the least talented, least beautiful, and least capable do not suffer from self-esteem problems. Like other writers of his era, who were worried about the "dumbing down" effects of media such as television, Vonnegut is parodying the 1950s and early-1960s American emphasis on mindless conformity. He is arguing that people of talent need to be recognized because their contributions, even if they are as intangible as the beauty of a ballet dance.