Sen. Mike Lee's opposition to the Affordable Care Act ultimately rests on his interpretation of the Constitution. He asserts that none of the federal government's enumerated powers in Article 1 Section 8 authorize such a law, and he appeals to the "Founders' intent" to justify his position.
Let's look closely at the Founders' intent. In 1791, Alexander Hamilton, who helped write the Constitution, commented on Article 1.8, which grants Congress the power to levy taxes "to provide for the common defense and general welfare of the United States."
Hamilton says that the power of Congress "to raise money is plenary and indefinite; and the objects to which it may be appropriated are no less comprehensive, than the payment of the public debts and the providing for the common defence and 'general welfare.' The terms 'general welfare' were doubtless intended to signify more than was expressed or imported … otherwise numerous exigencies incident to the affairs of a nation would have been left without a provision. The phrase is as comprehensive as any that could have been used. … It is therefore of necessity left to the discretion of the national legislature, to pronounce upon the objects which concern the general welfare." (Alexander Hamilton, "Report on Manufactures," Dec. 5, 1791.)
In simpler terms, Hamilton argues that the meaning of "general welfare" is up to Congress. It's easy to argue that the health of the public is an "exigency incident to the affairs of a Nation." Diseases become epidemics, poor public health undermines our national security, the medical and dental problems of the poor become an unacceptable moral and financial burden on us all. So according to Hamilton (a Founder), if Congress decides that the "general welfare" of the nation is at stake, it has the constitutional authority to legislate health care.
When it comes to the Founders' intent, I will take Alexander Hamilton's views over Mike Lee's.