Medicare has been thoroughly fucked with and partially privatized. Medicaid on the other hand is no copay (even on prescriptions), free at point of use, and still privatized, but less so.

Fundamentally what we actually need is a "federal health insurance corporation" which receives full funding from the federal government to provide single payer health insurance to all citizens and to interface with insurers and payers for healthcare of visitors. Something more akin to the NHS but independent enough that politicians can make them cover something, but can't make them not cover it. Currently we just really don't have anything like that. Though Washington, Colorado, and Nevada do have public option health insurers now.