My friend, Walker Wright, made me aware of an interesting article by Tim Bayne, "A Participatory Model of the Atonement"--it is a good discussion of the participatory model one finds in texts such as Col 1:24 in the New Testament. Here is one section on the problems of many deontic models of atonement:
Consider also another intimate relationship, that between children and parents. Although there may be some room for a deontological approach to the parent-child relationship, this is surely not how this relationship ought to be understood in the first instance. Children may have an obligation to care for their parents in old age simply because they are their parents, but their primary motivation and ground for such activity ought surely to be that of love. Similarly, parents may have obligations to care for their children simply because they are their children, but their primary motivation here should be based in the love they have for them. At the very least, if the obligation has to play an important motivational or explanatory role, there is something deeply wrong with the relationship. Invoking deontological language in a last-ditch effort to fix what is broken is unlikely to mend an intimate relationship, and may well sour it further.
So, too, it seems to us, to conceive of restoring a broken relationship between a person and God in terms of compliance with obligations is to do grave injustice to scripture and to Christian tradition. According to the prophets, God desires mercy not compliance with ritual commands. Compliance with obligations is a consequence of atonement [and] not its ground (Isaiah 1:11ff, Hosea 6:6, Matthew 9:13, Romans 3:20, Galatians 2:16) (p. 7)