In the story “Harrison Bergeron” by Kurt Vonnegut Jr. who is running the government ?

There isn't a specific party mentioned. It is some sort of autocratic "Orwellian-like" party that has turned America into a dystopia. The current Handicapper General, Diana Moon Glampers, and her team of agents have developed several forms of "handicaps." Beautiful people are forced to wear masks, athletic people have to carry weights, and intelligent people have to wear radios in their ears that interrupt thoughts with loud noises.