It's not completely inelastic, but it's pretty damn close. There is already a severe shortage of physicians & other health care personnel, and it takes years to educate new ones. The average doctor probably works about 60 hours a week as it is. He's not going to work more if you find someone who's willing to pay the bill for people who aren't currently getting "adequate" health care. But he will very likely charge more.
Have you seen the explosion in MRI centers? Urgent care centers?
The supply of doctors is restricted by a professional guild. The price doctors can charge is limited by HMOs and the Feds and other bureaucracies. So the money goes into other avenues like labs and MRI centers, which are often owned by docs.
Our entire health care industry is a socialist nightmare, but it's still better than in other countries where the socialism is even more pervasive.