Some further thoughts:
1) It occurs to me that if a VAT were to be attempted in this country, some individual state would have to be the first to try it, then you could talk about taking it national if it worked. That's the great thing about federalism: an idea can be tried on a small scale before we put it over the whole country. If it turns out to be a flop, the damage has at least been contained.
2) Since it's a tax on a company's added value to a product or service (in other words, profits) it could possibly replace not only retail sales taxes but also taxes on corporate income. Although this would probably mean the rate would have to be higher to get the same revenues, you would still get some consolidation/simplification out of it, and that's probably a good thing overall.
3) It would be prone to some of the same political problems that retail sales taxes and corporate income taxes have, such as every last business sector lobbying for exceptions, deductions or lower rates. And then we'd get all sorts of horrible distortions finding their way into the economy along with the potential for the same bloated tax code we have now, just administered differently.
4) In terms of raw politics, you can't base a tax structure entirely upon it. Even if you think a pure VAT would work on the economic merits I'm undecided and honestly out of my league on that question small-d democratic considerations would demand some progressive element be put into the federal tax system. And that means someone would start calling for a universal rebate which leads us to that whole labor incentives problem. And then we'd see a really bad idea coming in through the back door. Even if you're against it in theory, any inefficiency introduced by a separate progressive income tax would still be a small price to pay in order to stop the emergence of an enormous welfare underclass.