I'm goign through this with my STBXH. When he left, he promised to payhalf the marital debt ($10,000 in credit cards in MY name). Then, when he got a lawyer, he changed his mind. Basically, I could be divorced now if I agreed to let him walk away from the marriage free and clear - without holding him to his (more then fair) agreement to split the debt.
It's been a very difficult decision, but I have two children to raise and a limited income. He left because he was having an affair and left not only me (very pregnant), but also his children and my older son in the lurch, confused and hurt.
To me, it would be such a major betrayal on my part to let him walk away, completely unfettered with consequence or responsibility.... you know what I mean?
Quite honestly, I'd be happy if he'd just agree that he was responsible for the debt, sign the divorce papers (saying such) and the custody papers and get it over with - even if he never paid a penny. Just for him to admit that he DOES carry the responsibility of some of the marital debt he created. For him to admit he DOES have some consequence for his behaviors. YKWIM?