Sounds like a takeoff on 12:01. I think the earliest repeating day story I've come across was from The Shadow radio series.
Awake is not a repeating day story. The main character had an accident. He awakes and finds his wife alive, son dead. He sleeps, awakes and finds his son alive, wife dead. Each each scenario, life goes on -- but without the corresponding family member. Each time he sleeps and awakes, he finds himself in one alternate reality, then he sleeps and awakes in the other reality.
This
Youtube trailer should give you a better idea of the series.
I finally got around to watching the preview.
Awake seems to be an interesting concept. Doesn't look like my cup of tea, though.
For a series, that is.