We’ve all seen movies where the change the protagonist undergoes does not seem earned and it makes the whole movie seem phony and hollow. One of the things that makes Groundhog Day so great is that a person who starts out genuinely horrible at the beginning transforms into a really good person by the end and the audience completely buys it. At any point along the way, the story could very easily jump off the rails of credulity, but it never does. A nearly perfect little movie.
I wouldn’t describe Bill Murray’s character at the beginning as “horrible.” He doesn’t even seem to rise to that level. He’s just an asshole. Harmless, but completely unpleasant. A person you would avoid if at all possible. You’d cross the street to avoid him (unless, of course, you were Ned “the Head” “Needlenose Ned” Ryerson).