The government doesn't produce anything.
Well, that's not entirely accurate. The government produces services like law and order, restraint, or defense. But not things like cheese, bicycles, or galoshes. Or medicine, for that matter. Well, except for military doctors and corpsmen. They are government employees that produce medicine. Still, that's not what normal people think of when someone says "publicly provided health care." Or more typically, when somebody says "single payer."
"Single payer," you see, is a euphemism for state-run, state-funded provision. In the US, we have state-run, state-funded public education. Single-payer education, if you will. Except that the running and the funding are separate things. This is the point that charter school boosters make: state-run schools are a monopoly and are vulnerable to all the bad downside risks (and they are risks, not certainties) that come with monopoly. If the democracy chooses to mandate universal education, then is it not more humane to at least attempt to break the monopoly power that state provision of education has? Isn't that why we have anti-trust statutes enforced by the FTC?
The chief error I recall hearing in 2008 was that the PPACA was going to turn the nation's hospitals into dingier versions of the VA. Folks on the right pointed to some horror stories from the UK and Canada, citing these as evidence against single-payer. Of course, that's not the issue, since the UK and Canada are both single-payer and single-provider. What if it's the single-provider that's the problem? What if the NHS suffers the same fragility threats as America's school districts?
Single-payer really isn't all that scary without single-provider. Without competitive alternatives available, state-run enterprises have a rather shocking track record of quickly falling into grave obsolescence, staffed by sinecures, stifled by imprudent re-investment. If for whatever reason, undergirded by whatever moral intuitions private funding is not politically feasable, the attentive voter should be quite keen indeed to keep the distinction between funding and provision clear.
Don't get fooled again. Your BATNA can't handle it.