Given the federal Constitution's silence about public healthcare, the 10th Amendment automatically reserves government power to regulate healthcare to the states, not the Oval Office and Congress.  So the federal government has no constitutional authority to regulate and lay taxes for public healthcare.

In fact, regarding intrastate commerce in general, Thomas Jefferson clearly indicated that Congress has no power to regulate intrastate commerce.

"For the power given to Congress by the Constitution does not extend to the internal regulation of the commerce of a State, (that is to say of the commerce between citizen and citizen,) which remain exclusively with its own legislature; but to its external commerce only, that is to say, its commerce with another State, or with foreign nations, or with the Indian tribes." --Thomas Jefferson, Jefferson's Opinion on the Constitutionality of a National Bank : 1791. avalon.law.yale.edu/18th_century/bank-tj.asp

But more specifically to healthcare, the USSC has already decided that Congress has no authority to regulate medicine.

"Direct control of medical practice in the states is obviously beyond the power of Congress." --Linder v. United States, 1925. http://supreme.justia.com/us/268/5/case.html

The bottom line is that perversions of the Commerce clause (Article I, Section 8, Clause 3) by FDR's pro-big federal government, outcome-driven justices is what has gotten us into the big federal government mess that we now have.