In "Harrison Bergeron," who is running the government?
It is heavily hinted that the government is no longer a representational republic, although it still falls under the Constitution. The implication is that there is a more socialist-style of governing, with secret police operating for the government to inform on people attempting to subvert the laws in place. As explained in the intro paragraph, total equality of outcome has been legislated into the Constitution, with "agents of the United States Handicapper General" keeping both the peace and preventing people from trying to remove or alter their handicaps.
"I mean -- you don't compete with anybody around here. You just sit around."
"If I tried to get away with it," said George, "then other people'd get away with it -- and pretty soon we'd be right back to the dark ages again, with everybody competing against everybody else. You wouldn't like that, would you?"
(Vonnegut, "Harrison Bergeron," tnellen.com)
This seems to indicate that the government is more controlled by a dictator, rather than an elected President. Since everyone has to be equal under the law, an elected President would be as average as anyone else; this is not conducive to a productive nation, and instead if is in their best interests to find a leader who is more intelligent and more authoritative. Like Soviet Russia, the leaders are "more equal" than the citizens; an indication of this is the presence of the Handicapper General herself, who kills Harrison with perfect aim, unhindered by handicaps.