Among the various justifications for President Obama's/the Democratic Congress's "public option" health care reforms is the belief that it would reduce the "cost of health care" for the majority of families (while increasing taxes on only the rich, but that's not important right now). I'm hesitant to call them "disingenuous", since "cost = price" and "health care = medical care" for most people, so let's call them "nomenclaturally unsound".
Taking the second point first, "health care" is brushing your teeth, eating your veggies, riding a bicycle with your helmet on, and avoiding getting into fifty-little-red-wagon accidents--basically all the stuff mothers and fathers stereotypically nag their kids about. "Medical care" is what the doctor, dentist, surgeon, etc. are for--treating those infections and injuries that come up when health care fails and you get hurt.
(As a side-bar, and not a particularly important one, "preventative care" (screenings, regular physicals, etc.) strikes me as much like national defense...that is, plenty useful in the minority of cases where they apply, but not the first thing I think of when I think of "saving money on health care".)
Addressing the first point, as anyone who's ever played a management simulation game (even one as simple as "Lemonade Stand", which we can use as an example) will tell you, "prices" are infinitely flexible--you can set the price of your lemonade from one cent to two dollars a cup, or simply give them away for free. "Costs" are a completely different thing, as you'll have to spend money--that is, make an initial investment, a cost--to get the lemons, sugar, ice, etc., required to make the lemonade. If your "price" is not enough to recoup your "cost", you can either take the loss as debt or alter the formula of your lemonade to fit your price--using less lemon and sugar per gallon, for example.
The same rules apply to medical care. With respect to Obama and Congress, it is not their place to reduce the cost of medical care; that job belongs to the pharmacist who develops his "over-the-counter Cancer Buster" drug (an obvious joke) in a mass-production-capable way, or even to the educator who develops a curriculum to fast-track medical students, reducing the time required for their training (for time is money, a limited resource, after all). What the government can do is work with the price of medical care, e.g. with taxpayer subsidies or by mere price-control fiat. If this is not enough to pay the costs of that care, however, then the quality, timeliness, or some other factor will be exchanged to compensate--perhaps a steadily reducing MRI-per-capita count, or that "Cancer Buster" drug that never gets developed.