I think Bill actually wanted to divulge into the more darker aspects of reliving the same day over again (murder, torture, robbing banks, etc), but Harold Ramis just wanted to stick to the script and avoid all of that. They actually had a huge argument over it and that (along with the fact that Bill was going through a hard divorce) is what caused them to not talk after making this movie for a long time.
The movie deserves some sort of remake/TV show which goes into the more darker themes