Add in that people will have more take-home pay (no income tax or FICA taken out of their checks) and lower interest rates, and I'd be more worried about the fate of landlords, because all of their customers will be flocking to buy houses.
Except that in some places (Texas) illegals currently build houses and they don't pay taxes. That is why you can occasionally find a new home for $50/sf here. Plus the amount of untaxed cash deals is staggering. As much as preventing drugs, civil forfieture is probably meant to increase the cost of doing business tax free, but that is another subject.
I support the idea behind a national sales tax, I am just skeptical of this proposal.