I have been playing 4e for almost 3 years now and have noticed that the average character has the capacity to take massive amounts of damage each day without any ill effects the next day. I have even worked out through math that the average fighter can, over the course of one day, take almost four times his hit points in damage and still be at full health at the end of the day. That is without counting in the fact that leader types grant even greater levels of damage-taking abilities. Even if a character is at 1 hp at the end of the day, he wakes up at full hp and is ready to go as if nothing happened the previous day.
4e has no "carry over damage," unlike previous D&D editions that had damage heal slowly over time, with magic healing, and with potions.
It is not my intention to add a death spiral to D&D; that is not something that would be beneficial to the game and it would change the game entirely. What I am looking for is a way to adjust the healing and damage system in place to make it feel more like past editions.