1) Assuming that health care is, in fact, scarce, rationing would be no help. Rationing creates scarcity. It also creates black markets for what resources are available. In time of total war or natural disaster, rationing of resources -- health care, sugar, waste materials, whatever -- might be justified as a form of social triage; however, as soon as the emergency is over, rationing impedes recovery and fosters corruption.
The Lake Tanganyika Basin is the most underserved area of the globe as regards health care. There is only one health care professional (doctors, nurses) per four million people. Rationing what health care is available would be useless. The answer is to increase the availability of health care to that area by any means possible. Compare the Tanganyika Basin with the USA to contemplate point #2.
2) Far from being scarce, health care in the USA (doctors, nurses, specialists, hospital beds, drugs, prostheses, treatments of all sorts) is the most plentiful of any society on earth. Wait times for procedures are low because we have amazing availability. In fact, in some communities, there are too many hospital beds competing for patients.
The problem we have is price, not availability. The easiest single thing we could do to make prices come down would be to reduce the costs of malpractice insurance through tort reform. But trial lawyers are the single biggest donor constituency of the Democratic Party, so that's out. If you doubt this, consider the availability and cost of veterinary care: prices are low for the services of comparably trained professionals -- and this, without insurance, even -- in part because vets' malpractice costs are negligible.
I wouldn't give the government control over my pets' health care. Why should I want them to control my family's health care? Obama is wrong, twice-over.