Segnosaur
Penultimate Amazing
Ok, 2 things...This would be a government-run plan, along the lines of Medicare-for-all, but with a national-service component (so a VA expansion along with the Medicare expansion). Participation would be mandatory; there would be employer payroll deductions, like there are now for Medicare. There would naturally be exemptions for disability or unemployment, but for the most part it would be a pay-as-you-go system.
The problem with payroll deductions is that you have to deal with 1) people that are self-employed, and 2) people that are part time/work minimal hours, and thus wouldn't be able to make their minimum payments. (Not insurmountable problems but still need to be considered.) You may almost be better to take things out of general tax revenue rather than payroll deductions.
More importantly... if its a government-run health care, are you also going to allow private hospitals to function along side the public (government funded) ones?
The best health care systems in the world seem to have some sort of mix of public and private. Although there are accusations that allowing private care is somehow "unfairly jumping the queue" (i.e. people who pay more get faster access), in practice it is a great benefit, since it allows your health care system to be more responsive. Canada has a (more or less) single payer system (funded through tax revenues, but delivered privately) , and we have significant problems with wait lists.