OK, I feel like the liberal at the Bill Gothard convention, but I believe that the verse is NOT a commentary on debt in the financial sense.
Rather I believe it is a comment on spiritual and personal debts, that spiritually we are to be indebted to no one other than God, and personally we are to love one another and not be indebted to one another.
In other words, we do good works for others out of our love for them and not because "he was the person who led me to Christ," or "she was a good friend to my mother-in-law's cousin."
If any of you know about Middle Eastern and Eastern cultures, a common concept is that when someone helps you, befriends you, gets you a place to work, whatever, that "you are in that person's debt" until you can return the kindness. Many times, you would be "indebted" to that person for life.
Obviously, especially if the person held out the "debt" for a small favor to be a lifetime of being there for that person or doing something against your principles for him/her, then resentment would creep into the picture.
I believe that passage in context simply means that Christians should not be caught up in an endless cycle of spiritual and personal obligation centering around doing good deeds for others, when those deeds should be done out of love for God and others, not duty.