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You’re ignoring my suggestion that the primary funding source will be a payroll tax roughly equal to what employers now pay to insure their workers.
Because that funding source wouldn't be close to enough. That kind of a payroll tax would only cover about 60% of what is currently paid out in private health insurance, and probably not even half of what you need to raise.
Employer health insurance programs only account for about 80% of private health insurance to begin with (the rest is individual market and direct purchase of insurance products). Employers only pay about 3/4 of that, so you end up with the employer contribution only constituting about 60%. Once you add in the uninsured and underinsured (or self-insured), you're at less than 50% of the total.
You know, there are lots of devils in the details, but what every other industrialized country in the world does kind of shines the light on what should be done.
Every other industrialized country has taxes in place to pay for it. The problem is the transition. Everyone's in their current position - they pay X for health care, and they receive Y in health care. There's no possible way to manage a transition from the current system to the new system without a very large number of people seeing either X increase or Y fall. There are too many net losers in the conversion, because there a lot of people who today pay relatively little and get very good health care coverage (those "cadillac plan" folks and a lot of retirees).