Actually there is competition: competition for who can cover healthy patients, while dumping sick patients into the great pool of uninsured, or onto competitors. Competitive markets in health insurance structurally lead to the results we are seeing.
> The concept of universal health care is popular in the U.S. When the question is put to them in real and straightforward terms, rather than a choice between 'government control' versus 'free enterprise', they overwhelmingly choose universal/single payer.
Not as straightforward as you think. They will the end, but not neccesarily the means. That is, when you say "universal health care" a lot of people think of our present system with the holes plugged. If you bring up the idea of states or government funding replacing most private health insurance, the choice turns around overwhelmingly. Explain a bit more, and people support the idea. A single payer system could win; but you need education first. Put single payer on the ballot in most states without prior education, and the other side can easily buy your defeat.
But I do think you are right that people are fundamentally on our side. Single payer health is the only issue on which I have ever won "converts". Give me fifteen minutes with someone who supports "universal healthcare" but does not like the sound of public funding replacing private insurance companies, and usually I can turn him or her around. People don't normally change their minds in response to rational argument; it has to mean that on some level they believed it all along.