The problem with this whole argument [about health care in the US, and the potential for some kind of national health care] is that there are already so many perverse incentives and so much actuarial idiocy in the US system that it's hard to sort out anything in the data. Still, there are some obvious things:
(1) corporations can buy insurance with pre-tax dollars, individuals must use post-tax dollars. This means individual insurance is at minimum about 16 percent more expensive than company-paid insurance.
(A single-payer system would eliminate this problem, since it would all be paid for with some kind of tax; given the other examples of government efficiency, I wonder if the advantage wouldn't be lost through inefficiencies.)
(2) there's no easy way to form a pool of risk; this means small companies have to pay relatively more per person.
(A single-payer system enlarges the risk pool, but so would allowing insurance companies to treat their entire policy base as a single risk pool. The single-payer risk pool is bigger than any individual company's policy base, but the marginal advantage becomes vanishingly small. This is why relatively big companies like Sun and IBM "self-insure": it's cheaper to simply pay the costs than to buy insurance. The mathematics of this aren't instantly obvious, but it can be proven.)
(3) HIPAA etc regulations make it nearly prohibitive for small companies to get health insurace if they can afford it.
(I can't decide if I think single-payer would change this; cynically, it seems more likely the companies would simply have the whole burden of HIPAA imposed on them no matter what, even the small ones that had avoided it before.)
(2 and 3, by the way, are the base of "employee leasing" companies like Administaff, which outsources the whole HR thing ... but adds profit margin to the deal. It's a sign of the perverse incentives involved that the economies of scale mean that the complications of setting up Administaff's HR operation in a whole separate company, including effective double taxation of the costs, plus a good bit of margin, is still far less expensive than doing small-business insurance and HR.)
(4) The lack of any predictable bounds on malpractice awards means that the mathematical risk per doctor is very very high, and as a result, malpractice insurance is extremely expensive.
(This is easily proven mathematically, which is probably why the discussion almost always is suborned with discussions of "incompetent doctors and greedy insurance companies trying to cheat sick babies". The only way a single-payer system could help with this is if it included limits on malpractice awards; since you could simply limit malpractice awards without the other baggage, you can't call this an advantage of single-payer.)
(5) the malpractice poroblem means that lots of defensive procedures and tests are performed, which raises costs.
(Many studies about this, but it's easily confirmed simply by asking any random doctor. Single payer would have at best no effect on this without malpractice reform.)
(6) the tax problems and risk-pool regulations mentioned above mean that insured people are nearly wholly insulated from medical costs. There is no economic incentive to hold the costs down.
(Single payer would eliminate what little connectin people have now.)
(7) medicare and required-coverage regulations make treating many insurance patients uneconomic -- which means insurance companies and doctors have to transfer costs to people who are paying privately, or to better insurance.
(Either single-payer wouldn't change this, or single-payer would have to reduce coverage over the current regulations. No obvious advantage to single-payer there.)
(8) the legal requirements that everyone be treated in emergency rooms, regardless of ability to pay, mean that the costs of emergency treatment are transferred to private patients and the insured.
(Single-payer just means the transfers happen in Washington, instead of in the provider's accounting department. The only way single-payer could improve this situation is if the costs of single-payer could be reduced below the costs of making an on-paper transaction in an accounting office.)