I read the story in the early '70's, in a hard-cover anthology that was passed down from my father. I don't think he was reading science fiction at that point and my belief is that the book was at least a decade old. It is not Groundhog Day.
In the story, the protagonist is a man who is a stereotypical office worker as perceived in the 50's or '60's. Every day he has exactly the same experience. He wakes up, gets dressed for work, he eats breakfast, spills his coffee on his shirt and has to change it. He is late for work and has to make excuses, tells the same corny joke to his secretary, is dressed down by his boss, etc.
Every day is exactly the same. No variation is possible, at least in externalities. He can have different thoughts, but cannot say anything different or do anything different. Gradually he becomes aware of the presence of other beings observing him, and laughing at various things.
He eventually comes to the conclusion that he is in a kind of museum exhibit, i.e. "A Day In The Life Of A Human Being."