Assuming we're talking about the cleric class, I have an easy answer. With the Warlord, it's a bit more complicated, but still justifiable with a little bit of mental gymnastics.
First off the cleric. Let's say the cleric channels healing energy whenever he rolls a natural 20. This reflects the cleric "having his deity's favor." The precedent for this is that in Saga, a character who rolls a 20 on his "use the force" check gets his used powers back, because said roll means "the force is with him." To reflect the mercurial nature of a cleric having his god's favor, they could institute a similar mechanic.
Alternatively, the cleric could be totally driven by the power of his god, and so when he strikes a blow against the enemies of his god, divine energy flows forth from him. That's a little more predictable than waiting for a good roll...and just as justifiable.
With the Warlord, it's a pretty similar logic, but it relies on the Warlord's fellows being "revived" when he strikes a mighty blow. This relies heavily on the "second wind" or "morale" nature of hit points, and so bothers some people's suspension of disbelief. Personally, I find it easier to believe that hit points only reflect "one's ability to survive attacks." And until the character is at (or below) 0 hit points, he just hasn't sustained any serious injuries.
Of course, that would require the names of the healing spells to be changed, which I think is happening anyway. Magical healing, especially regarding low-level characters (heroic or otherwise) and the efficacy of "Cure Light Wounds," is the only thing that doesn't easily fit the notion of "hit points as abstract damage." As such, IMO, it's the magic that should be changed.