Can the U.S. have a national health system? Why or why not? What role does the 10th Amendment to the U.S. Constitution play?

Debates about healthcare reform almost universally compare the U.S. system to that of the U.K. or Canada, national health systems. Can the U.S. have a national health system? Why or why not? What role does the 10th Amendment to the U.S. Constitution play?