Earth to Herman Cain: The third "9" in your plan is unconstitutional

Most of us have heard by now of Herman Cain's infamous 9-9-9 tax plan, where he would favor a 9% federal income tax, 9% federal corporate tax, and a 9% federal sales tax. It's bad enough that he wants to give the feds a new tax source*, but he needs to know that a federal sales tax is unconstitutional!
Here is the evidence:

Article I, Section 9, Clause 4 of the U.S. Constitution:

No capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or Enumeration herein before directed to be taken.

That clause was amended by the Sixteenth Amendment (which itself ought to be repealed):

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.

Note that the power granted to Congress is limited to income taxes. For any other direct tax, Article I, Section 9, Clause 4 still applies.

There is another reason that we should oppose the 9-9-9 plan. Can there be anything good for the middle class to have the feds tax money going in and going out.** Herman Cain's plan taxes individuals twice, income and sales tax, and it taxes corporations twice, corporate and sales tax.
I think Michelle Bachmann had the right idea. Turn the numbers upside down and you get 6-6-6 -- the devil is in the details.
* Fox News says that we are still paying taxes based on a bill to finance the Spanish-American War!
** Of course, Ohio has been doing this to us since the income tax was adopted in 1973, but we could still repeal it if we so desired. Getting the feds to repeal a tax is almost impossible.