The word "debt" in the phrase "sleep debt" is mostly a metaphor. It is sometimes used to describe the effect(s) of a loss of sleep loss on future sleep or future actions. Thought of that way, it may be odd to have a postition on whether the metaphor "exists." It is a way to describe something, or many things, that happen when sleep is "lost." Although, that too can be considered a metaphor, since sleep is not so much misplaced and then later "found." It may be similar with the phrase "sleep pressure."
Whether one likes the metaphor or not, the effects of sleep loss on human functions are still being studied around the world in various ways:
http://cdn.intechopen.com/pdfs/36039/In ... humans.pdf
It appears that SWS may have a pressure/debt/rebound/recovery component, much like REM, depending on age:
http://www.plosone.org/article/info%3Ad ... ne.0043224
My position is that if one sleeps badly for a while, one's body/brain will do its best to sleep well, if it gets a chance to. I think that can be as true long-term as it is short-term.
But as far as what the sleep pros usually mean by sleep debt in the context of long-term troubles, maybe the best definition is the following simple one:
Sleep debt may be defined as the cumulative hours of sleep loss with respect to the subject-specific daily need for sleep.
http://www.med.upenn.edu/uep/user_docum ... 1_2003.pdf
In other words, if you get less sleep than you need, you end up paying for it, one way or another.