What is he only needs a little time to get back on his feet.
I don't have kids, but I was out of work for a while and I really had to cut back. Trust me, this economy isn't working for everybody. Has the father been paying all along, only stopping under real pressure? If he falls of the ledge, and has liens against him it can HURT his job prospects, make him desperate and LESS likely to get hired. This can be a positive, life-afirming turn-around or it can be the straw that breaks him.
State like California can take his driver's license away, effectively turning him into a bum. Excellent for a bitter revenge, not so good if you want him to be a father to your children.
Use the State as your enforcer with care. It should be the last resort to go after a scoundrel because it can kill a man's ability to earn money, and live a normal life.