I'll probably get some details wrong (at work and should be working), so cut me some slack:
The private sector is really good at a few things, the best of which is making money. But the way they do this makes them bad at "serving public good" because that generally costs money without direct return. Making sure every child gets an education isn't directly optimal for the private sector, for example, because the ability to pay is a barrier to some families. So, the private sector would be best at making sure the people who can pay are well-educated (competition takes care of that), but some families will never be able to beat the barrier to entry. In that respect, the private sector is ill-suited to the task (making sure everyone is educated) because it's not in their wheelhouse. One way to get around this is to have "the government" act as the surrogate customer, and purchase an education for everyone, because they have (in the closed system of the physical bounds of the country) the most buying power. You can't beat their volume, so you accept their prices.
To bring it back to health care: "health insurance for everyone" is a similar goal as "education for everyone", but there's the added wrinkle of the current situation which is where people aren't buying health care directly. The employers have been using their buying power as leverage to entice workers. Of course, unless you replace a medium-sized surrogate buyer (employers) with a large-sized surrogate buyer ("the government"), you're left with individuals with little buying power again facing barriers to entry, because private industry and competition are not good at solving the "absolutely everyone" problem, they're good solving at the "best for what you pay" problem. By compromising and keeping employers involved in the buying market for insurance without also adding a single payer option where the government acts as a buyer with superior negotiating power, the current healthcare law gives us potentially the worst of both worlds.
Now, as I understand it, the state-run markets are meant to act as surrogate buyers for individuals, but by letting states opt in or out, people in opt-out states have no buying power, and can't negotiate a good deal for themselves. And why should the insurance companies deal with small fry when their goal isn't to insure eveyone, but to make the most money? That's their purpose.
Basically, every concession made to pass the bill made the bill worse, because conservatives also don't have public good in mind; their goal is to ensure that corporations can act unfettered, without thinking about whether unfettered privatization will lead to greater public good or not.