As David Henderson observes, it's nice to see that the Economic Report of the President actually includes facts and sources. Of course, that opens the analysis up to criticism it wouldn't otherwise face.
The Report notes four sources of inefficiency in health insurance markets: adverse selection, moral hazard, the Samaritan's dilemma, and incomplete insurance contracts. But as Henderson points out, the Report itself draws attention to the market solutions for the first two of these -- and oddly condemns them. (Risk-rating is the market response to adverse selection, and high deductibles and co-insurance are the market response to moral hazard.) It's worth adding that government policies like community rating and mandated benefits exacerbate adverse selection, and government-provided care and insurance exacerbate moral hazard.
We should also cast a skeptical eye on the Samaritan's Dilemma -- that is, the willingness of the citizenry to provide care for people who can't or won't provide for themselves, which encourages free-riding. While this is a real issue (as are the other three cited inefficiencies), what is its magnitude? The Report says uncompensated care for the uninsured was $56 billion in 2008. That sounds like a lot. But the Report also says (elsewhere) total expenditures on healthcare in 2009 were $2.5 trillion. Assuming the 2008 and 2009 numbers are relatively close, we can do the math and conclude that uncompensated care for the uninsured is less than 3% of all health expenditures.
For what it's worth, I think the Report's fourth source of inefficiency, incomplete contracts, is probably the most serious challenge for private insurance markets. That is, aside from the various government policies that hobble them now.