[Brad DeLong is] obviously assuming that there's no substitution effect in the demand for health care - that the production function is Leontief in the health care direction and that any measured price elasticity of demand comes strictly from the income effect. There are obviously a number of estimates of the price elasticity of demand for care in the literature, but the most commonly quoted price elasticity is probably the one found by the RAND Health Insurance Experiment (HIE) in the 1970s; roughly -.20. I'm inclined to think that these days that would be an understimate, for various reasons, but that's the RAND HIE number.
What's interesting in regard to your post is the structure of the HIE. The RAND experimenters randomized a few thousand participants into a number of different health insurance plans - the difference between plans was primarily in terms of co-payments and deductable levels. The problem they faced was that a lot of the participants already had health insurance plans, and the randomization process might assign an individual to a plan which provided less generous coverage (higher co-payments, for example) than their existing plan. Individuals who found themselves in that situation were likely to refuse to participate.
To get around the problem, the RAND group calculated, for each individual in the experiment, the maximum excess amount they might have to pay as a result of being assigned to whichever plan they'd been randomized into.
They then made a side payment of this amount to anyone for whom it was positive. This meant that everybody was guaranteed that they would have enough income to buy the same bundle of goods as before, even if, as a result of being assigned to a less generous plan, they faced higher prices for health care than before. In other words, the HIE's calculated price elasticity of demand was a compensated elasticity.
It wasn't a perfect, intermediate micro textbook compensation mechanism, of course, because as far as I know they didn't tax people who were randomized into plans which were more generous than the ones they were already enrolled in, but it was probably as close to a Hicksian compensation mechanism as you're ever likely actually to observe.
So the most often quoted price elasticity of demand for health care is closer to being a Hicksian than a Marshallian elasticity, and, contrary to Brad DeLong's hypothesis, it's not zero. Brad DeLong might be a top flight macroeconomist, but he doesn't seem to know the health economics literature particularly well.