http://data.worldbank.org/indicator/SH.XPD.PCAP
What you are suggesting is essentially that market failures have made private health care "too big to fail." Not a reasonable argument when public health is at stake.
Second, "lack of single-payer insurance" isn't why Americans overpay for health insurance. We have collusion between cartels of buyers and sellers (hospital chains and insurance companies) with secret price lists, funded by HR managers several hops away from the actual demand for services. It is probably enough to decouple insurance from employment. The Swiss, for instance, don't have a single-payer system, and they also pay far less than the US on health care.
(That latter argument, unlike the ones I've written about previously on this thread, actually does represent some of what I believe).