Kalni, you know that you can't "make" him take on the responsibility. You can suggest that it is a good idea, and try to encourage it. Though about the time you start to encourage it he probably sees it as nagging, and shuts off to the idea. He may well regret his choices later, but I don't know what you can do about it.
For now, I think you should wait and see what the lawyer tells him. Maybe it will help. Over here, if a parent has more physical custody, they may pay less child support. Maybe that would motivate him?