I had to contact 5 doctors before one accepted me as a new Medicare patient. I can imagine how much worse the situation is with medicaid and Obamacare.
It really depends where you are, for both Medicare and Medicaid.
Here we seem to have a lot of over-capacity, so every single primary and specialist (many hundreds) employed by all three hospitals is accepting both (unless they are accepting no new patients at all). There are hospital-affiliated clinics on what seems like every corner. The situation here is quite unusual, I take it.