Article I, sections 8 and 9 of the United States Constitution originally defined the taxing authority of the Federal Government…

(s8) The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States…(s9) No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken.

This creates two classes of taxes 1) “direct” taxes, which must be apportioned according to the census and 2) “indirect” taxes, e.g. taxes on commercial activity, transactions, etc. The Sixteenth Amendment to the Constitution extended the Federal taxing power to allow unapportioned taxes on income…

The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.

Income has been defined broadly by the United States Supreme Court, in the case of Commissioner v. Glenshaw Glass, as “instances of undeniable accessions to wealth, clearly realized, and over which the taxpayers have complete dominion”.
Not purchasing insurance is not income under the Court’s definition of income because the non-purchase of insurance is not “an undeniable accession to wealth” and therefore cannot be taxed under the Sixteenth Amendment’s grant of authority. Nor can the non-purchase of something meet the criteria of being subject to a directly apportioned or indirect tax, meaning that nothing in the Constitution allows the Federal government to tax an individual’s non-purchase of health insurance.
But the dubious constitutionality of the Federal health insurance mandate doesn’t end with this significant problem.
Congress and the President could have, in a clearly Constitutional manner, used its taxation power to influence the purchase of health insurance by creating a tax-deduction associated with the purchase of health insurance. This idea was, in fact, proposed by officials like President George W. Bush and United States Senator Ron Wyden. However, Congress chose not to go this route.
Given the current Federal tax code, such a deduction would extend an advantage already enjoyed by corporate purchasers of health insurance to individual purchasers of the same products. But in choosing not to create an individual deduction, and opting for a tax on non-behavior instead, Congress chose a mechanism of dubious Constitutionality specifically for the purpose of preserving an advantage that some purchasers of health insurance, i.e. the corporate ones, have over others.
One of the most fundamental purposes of a Constitution is to prevent a government from taking arbitrary actions that would favor some over others. When Congress stretches beyond its clearly enumerated powers, with the specific intent of preserving government created-advantages for some over others, it doubly violates the Constitution’s reason for being.