Jeffrey Toobin writing in the New Yorker:
The main argument that opponents of the health-care law have come up with is that the mandate regulates economic inactivity—i.e., not buying insurance—and the Commerce Clause allows only the regulation of economic activity. In the first appellate review of the law, last summer, the Sixth Circuit demolished that argument. The court pointed out that there are two unique characteristics of the market for health care: “(1) virtually everyone requires health care services at some unpredictable point; and (2) individuals receive health care services regardless of ability to pay.” Thus, there was no such thing as “inactivity” in the health-care market; everyone participates, even if he or she chooses not to buy insurance.
I don’t understand this argument. Health care is not health insurance. There is no inactivity in the health care market, but there is inactivity in the health insurance market. The law mandates health insurance purchases, not health care purchases. This does not seem to be a valid comparison.
Also, Ezra Klein writes regarding Paul Ryan’s budget plan:
It’s Medicaid and other health spending, which includes the Affordable Care Act, where Ryan really brings down the hammer: That category falls by 1.25 percent of GDP. So Ryan’s cuts to health care for the poor are almost twice the size of his cuts to health care for the old.
The plan cuts government-provided health insurance to the poor, not health care to the poor. The distinction is important because there is evidence that in some cases being uninsured is comparable to being on Medicare (see here, here, and here).
The Everyday Economist 
While health care is not health insurance, I believe the point is that you can receive health care without having to pay for it. To mandate health insurance then makes certain that costs won’t be completely borne on the hospital or whoever provides the services. However, you do make a good point about the words people use.
“While health care is not health insurance, I believe the point is that you can receive health care without having to pay for it. To mandate health insurance then makes certain that costs won’t be completely borne on the hospital or whoever provides the services.”
This is correct to the extent that one can afford health insurance. When a hospital treats an uninsured patient, it usually writes off the cost of the care and therefore taxpayers bear the cost. If the person cannot afford insurance and has Medicaid, the taxpayer is still on the hook for the cost. There is role for nuance here, but from a broad perspective these scenarios are the same.
The relevant questions are then: (a) how many of the uninsured can afford coverage, but do not purchase it?; and (b) how can we explain why those who can afford coverage choose not to purchase it?
If the answer to (a) is quite large, then your point has merit. However, I also think that the answer to (b) is very important for policy considerations. Unfortunately, studying this more interesting question is subject to significant difficulties and is likely substantially more complex than popular claims by the commentariat.
What’s missed by everyone, so far, is that people without health insurance will tend to seek health care, via urgent care/emergency ward, typically when an illness has reached the point of expensive remedy. There are many diseases, if caught early through routine check ups, which can be treated fairly easily and with minimal cost. With the certainty of coverage like Medicare, people are more likely to seek treatment early–thus creating less of a financial burden to tax payers at large.
Most, if not all, hospitals are obliged to care for people seeking urgent care. If the patient is indigent, the cost can either be held by the hospital–which in turns passes on the expense, in the form of higher rates, to those who can afford to pay–or pass it off as a business write-off to the taxpayer. http://articles.latimes.com/2012/mar/11/opinion/la-ed-health-law-plaintiff-20120311
So what if the bill ultimately goes to tax payers? They will pay less if medical insurance is available to all. Also, if you’re receiving Medicare benefits, chances are deductions are coming out of your Social Security benefits. So it’s not like it a total free ride.