No, you cannot quit a job, but if your tamagotchi never goes to work you will eventually get a new set of interviews; it seems your tamagotchi can get fired. ^_^
Actually, when your tamagotchi mates and you have a baby, you will get another set of applications for different jobs. Pick a new job which you have the highest skill points in, and then attempt to interview with the judges. With hope, you will get selected! Cross both of your fingers ^_^ !