Absolutely crazy! Disney World is busy everday, but any holidays, is especially busy, and Martin Luther King day is no exception. Be prepared to wait in line, and wait for everything else, because it will be more crowded than usual (on average I would say, about a 40 minute wait for rides).
Disney has visitors from all over the world so it will be just as busy as any other day. It is always good to get to amusement parks as early as possible to avoid crowds.