How will the government make healthcare -- or indeed any human endeavor ever before seen in history -- more efficient and less expensive? Examples please.
See my post above yours. Of particular note is the Singaporean example. It's certainly quite subjective whether you would consider it more "efficient", but it's a mathematical fact that it's less costly.
I think you're confusing "less costly" with "less pricey". Let's see if I can give an example.
We'll take all of your figures as true: The U.S. spends 16% of GNP on healthcare while other countries spend 12% or 8% or 4%. These facts tell us exactly zero about the cost of healthcare in the various countries. Why? Because they assume demand is exactly the same in all countries -- which we know it is not. It is like saying:
Bob's car needs $30 for a gasoline fill-up
Jack's car needs $45 for a gasoline fill-up
Mary's car needs $70 for a gasoline fill-up
Jill's car needs $105 for a gasoline fill-up...
...and then concluding that gasoline is more costly where Jill is. What if Bob's car is a sub-compact, Jack's is a midsize, Mary's is an SUV, and Jill's is a full-size pick-up truck? Then not only may the gasoline per unit cost the same but Jill's could actually be cheaper, right?
Demand affects the price of every kind of good and service, not excluding healthcare. Americans spend more on healthcare because they demand more.
All of this is of course entirely true. In fact reducing demand for healthcare has been a cornerstone of Singapore's state policy for reducing health expenditure- they've done that primarily through heavy co-payments for public funded healthcare(with private sector also mandated to make heavy use of them), thus giving consumers a strong incentive to restrain their consumption. Also by making medical treatment a thoroughly unpleasant experience(overworked and underpaid doctors, long waiting times, public hospitals that make hospitals here in Australia look downright pleasant).*
But I don't think you can reasonably say that lower demand explains all of it. Singapore has lower public health expenditures(3.3%) then the most comparable nation, Hong Kong(6%). Hong Kong happens to have a fairly strict cost control regime as well. All other developed countries have higher health expenditures then Hong Kong. So consider that... Singapore has
half the expenditures of its closest competitor.
*You might of course say that this is too high a price to pay for reduced healthcare expenditure. I don't necessarily disagree, and I'm not specifically advocating the Singaporean system. Just observing the fact that the government can potentially reduce health expenditure through cost controls and other measures... in fact America is unique in that it doesn't do so.