The offer that can not be refused in this film is for a psychiatrist to treat a domineering mob boss. Seems the Mafioso has a few psychological troubles that he wants to address, such as anger management and impulse control, the sort of things that often end up in someone sleeping with the fishes.
Billy Crystal and Robert DeNiro are both as excellent as you would expect from them, although the film is more whimsical than bust-a-gut funny.