Hon if you let things "bug" you that quickly (since you seemingly "just joined"), you're going to go through a lot of hard knocks in life. Be that as it may...if you're REAL, I'll give ya my two cents...even though you claimed to not want em.
If you TRULY don't make enough to support your kids and he left them with you, see if you qualify for state aid. THEY will go after him for support a.s.a.p. They'll want to get as much back as they can, and they do this by collecting the CS. You won't have to do anything. Otherwise, you'll need to do it yourself or get a lawyer and ask for temp emergency support. Doesn't mean he'll pay it, so be prepared to stand on your own if he doesn't. It's BEST to have a lawyer help you. For that, you can contact your local Legal Aid Society and see if you qualify for their assistance or reduced costs. If not, get a few free consults with various attorneys. Those should at least steer you in the right direction as to what to file and ask for.
Abandonment would be unlikely if he's had any contact with you and/or the children during the last 2 months. If he left and you've heard nothing, then you could ask for a divorce based on abandonment. It's only for the divorce mind you, and does nothing to change the legal standing with support and asset/debt division.
But you need to get the emergency CS hearing started a.s.a.p. Until it's ordered, he owes nothing, and they will generally only make him pay support from the filing date. So you need to get it filed.