I am a libertarian and aesthetically opposed to this idea, but I think realistically the least bad option would be universal coverage by a "designed to a price" public health system, maybe on par with the UK NHS, with better quality private care and private insurance for those who can afford it. Allow the government to provide scholarships (similar to ROTC) to promising studies to become doctors in the service, with MD salaries on the 80-150k range, and a focus on providing cost-effective routine and emergency care, and on cost effectively managing any expensive treatment. Roll Medicare into this. You could cut expenditures 50-80% while only reducing outcomes slightly, and cover everyone.
The AMA, industry, etc. would all be against this, but I think the total number of people employed in the medical industry is still low enough that "see, universal coverage" AND "50-80% cost savings" would win out politically over the libertarian arguments and the "death panels" arguments. By establishing that private health care can still exist, and be best in the world (unlike the Canadian system), reasonably wealthy people shouldn't be too opposed.
The risk is that a system of initially limited scope and budget would expand -- any given case where the public system didn't cover an illness might get up to a thousand constituents writing to their representatives. 1000 people highly motivated by an issue would trump 250 million people paying less than a cent each for the increase in cost in that one case. Eventually we would end up with a gold plated system like we have now. The only way I can think of preventing that would be for the US government to be starved of revenue (which it is working on!), or a constitutional amendment setting a certain standard of public care which cannot be legally exceeded.