[0] Medicare is our insurance program for old people, and I think also kicks in for those who are disabled at younger ages. Medicaid is the name for our HC program for the very poor. People get these mixed up because the names are so similar. Then of course there's our coverage for the active military and their families (Tricare) and VA healthcare coverage for retired military. And programs for other government employees, and their families. By the time you add it all up, a huge percentage of the US population is already covered by government healthcare schemes, actually, which is reflected in our spending enough on publicly-funded healthcare that we should be able to cover everyone with just that money, if our costs were similar to the rest of the OECD. Instead we still have the costs of private insurance and bills to individuals even when covered by healthcare (these can run into the five figures per year, easily, on top of insurance costs) and, for some of the above, huge expenses in addition to the costs of the government portion of the HC program.
[EDIT] Medicare gap coverage tends to run low-hundreds of dollars per person per month, in case that wasn't clear.
But past the premiums, there are deductibles, coinsurance (e.g. for hospital stays longer than 60 days), you still have to pay for medicines (how much varies), etc. See https://www.medicare.gov/your-medicare-costs/medicare-costs-... and the links from it for details.