This sounds like Philip Jose Farmer's noted short story "The Sliced-Crosswise Only-On-Tuesday World" which he later used as the inspiration for his "Dayworld" series, both about a future in which everyone sleeps in stasis except one day a week, as a solution to overpopulation. The original short story is a thwarted romance between two people who live on different days. I don't remember reading the novel, but according to Wikipedia, it features a group of outsiders trying to change the system.

This sounds like Philip Jose Farmer's noted short story "The Sliced-Crosswise Only-On-Tuesday World", which he later used as the inspiration for his "Dayworld" series. Both are about a future in which everyone sleeps in stasis except one day a week as a solution to overpopulation. The original short story is a thwarted romance between two people who live on different days. I don't remember reading the novel, but according to Wikipedia it features a group of outsiders trying to change the system.