Jhapaliketo,

You have not mentioned about your status. So I assume you are currently legally residing in US and don't have a green card. State government can provide medicaid to your baby based on your  income. If you fall under the poverty line (it differs from state to state) your baby will be eligible for the medicaid. Having a baby here in US doesn't ensure work permit for the parents. I don't thing you can claim work permit or green card based on your  baby being a US citizen. If that was the case then most of the illegal residents would have been legal. Last year I saw a program on MSNBC about people being deported from airport. One guy from some latin american country had been back home and was returning to US. He was deported from airport even though his daughter was in the US (She was a US citizen).
I am not discouraging you. Best thing is to contact a lawyer. As far as I know there is no such rule that parents get work permit solely because their child is born in the US, however, it might be easy (a plus point) for the parents to get permit if they have some other basis. I once again suggest you to contact a lawyer before you plan a baby.

Sparty