Ok, I'll second the individual vs. group thing being discussed in this article on Darwin vs. Smith vs. the Market. I'll really agree in it's application to housing, particularly in good school districts. But it doesn't apply to every aspect of consumption and so a "progressive consumption tax" isn't the magical fix that is claimed.
Where consumption is related to understood/believed future benefits and where there is a bidding up effect, then it is true. This is true of housing and education (both school districts and college tuition). To a lesser extent it may be true of some subset of things like clothing and food, though the extent to which other, beneficial market effects can react has meant that it really isn't true.
On the other hand there is a whole mess of consumption that doesn't really mean much or provide any meaningful advantage but does contribute positively to the economy. Buying an Xbox to sit next to a PS3 is an example. So is going on vacation, and tipping your server, and replacing your functional 7 year old car with a new one...and so is buying a yacht. But a rich person buying a yacht is, despite any ostentatious display we may find objectionable, giving business to a company that employs lots of people that are not rich.
In fact whenever we purchase things we are supporting employed workers. Often in many different places, from the store where we bought it (even an online one) to the company/companies responsible for transporting it around, to the company that produced it...even if the actual manufacture was in China, lots of employed people in this country were necessary to get that purchased item to the buyer.
Right now our economy is in a funk expressly because people are not making those purchases. A progressive consumption tax will make this worse. Moreover, we have lots of money sitting idle that would love to be invested, but can't because there are not enough opportunities because CONSUMPTION IS TOO LOW. A tax plan that lowers consumption and raises savings will make things worse, not better. A tax plan that eliminates goofy tax benefits for homeowners and student loan (sharks) would be a much better start. You know what that would look like? A progressive income tax with no deductions, and with the same rates applied to capital gains.
Perpetuation of wealth is not a good thing. It makes for idle resources, which means lower employment. There are two ways to have money work in the economy: investment and consumption. The tax system in the US benefits investment heavily but only benefits a subset of problematic consumption (mainly real estate and education). If the tax code evened out by directly benefiting neither, things would be better.
A last point here is that no matter how steeply progressive a consumption tax is it will be regressive in the end. If someone making $54k/year has to pay taxes on $12k of that ($30k deduction, plus $12k of savings) then that person is likely to pay a larger fraction of their income than a multimillionaire bringing in $400k/year in capital gains but who "only" needs to spend $70k of that. Someone spending $500k/year out of their $10M income would be taxed less heavily than the $54k/year family (yes, the exact rates matter, but it would need to be extreme to offset). Multi-millionaires and billionaires just don't spend a huge fraction of their income.