If you really want to consider having socialised healthcare, then you must also be prepared for the consequencies.
The healthcare system will become politicised, it will mean politicians appointing their placemen, and in the current US climate, that means idiots who actually know very little about healthcare and whose sole qualification is the ability to suck up to the leadership.
We in the UK tried that with Maggie Thatcher when she tried to make steps to de-nationalising healthcare, lets just say that it introduced a very expensive layer of managers, and produced very little in the way of useful outcomes, we are still having to deal with that legacy. The threat to our healthcare system that Thatcher posed is one significant, but not the only, reason she was removed from power.
Once you do have socialised medicine, you will also find it turns into a right of expectation, woe betide any politician who threatens it or screws it up.
Citizens generally like socialised healthcare, but it is very expensive, the system of sourcing healthcare services could be state funded treatment with private practiioners, through a mixture or private/nationlised, all the way to having a unified and single state suppiler of healthcare services, there are advantages and disadvantages to any system selected.
Next, you will need to work out how to pay for it, income tax will certainly have to rise, but there is one benefit, because it affect the politicians who will have an incentive to keep costs low, or keep value high in order to control taxation.
The financing of a national health service also has it problems, because resources are always limited and invidious choices have to be made, taxpayers will not provide a blank cheque which means costs of drugs will determine treatment instead of need.
How will you deal with those who work in the black economy, becuase realistically, this will become a big political issue, illegals who come to the US, pay little or no tax, but expect to have free medical treatment, it happens in the UK to a fairly limited extent, but in the US it would probably be a greater issue.
It would have a couple of huge advantages for workers, becuase they would become more employment mobile, instead of being tied down with certain employers due to the medical insurance, this in turn may well allow companies lower direct costs though indirect ones would rise.
There is likely to be a current huge unmet need for treatment, this has happened in most places where private medicine has been socialised, and it would take quite a few years to bring this demand down.
There is no reason to enforce compulsory state medicine, people should be free to insure themselves if they feel that is the best way to spend their money.
In the long run Socialised Healthcare does appear to cost less per capita, or GDP or whatever measure you choose, but then the quality of care is crucial too, for those who have the resources to obtain healthcare in the US, it would appear socialised healthcare is averaging quality downwards, but for those without cover its going to be a huge step up.