Quoting Ellie Shikari:" It's been a month since we split up and he hasn't been to see DD once, nor offered me any money to pay ... [snip!] ... I didn't want this for my baby... I feel like such a lousy mother right now even though it's not my fault he's an asshat."
You're not a lousy mother, he's just not making the right choices right now. Unfortunetely, you can't force someone to be a good, involved parent.
Child support to help you to raise her is for your child and is required in every state. This is for her, not you. She has two parents.
He may come around, or not, but she will be fine with you either way. You are a good mother who is doing the right thing by raising your daughter and loving her.