Fairtax: how does this math work out?

I'm really confused by the Fairtax system (http://www.fairtax.org/). As
I understand it, they want to get rid of the income tax altogether, and
raise the sales tax on items to 23%. They then refund taxpayers up to
the poverty level so that lower-income families don't pay very much in
taxation at all. They argue that low income, medium income, and high
income families will all benefit from lower taxation, while the
government will be able to increase the revenue it brings in from
taxation. Here's what I don't get:

Let's say Arnold Schwarzenegger loses his political position, and goes
back to making movies. Arnold made about 30 million the year before he
ran for governor. Under the current tax system, he pays something like
40% of his income back to Uncle Sam:

30 million *0.4 = 12 million paid in income tax, leaving him with 18
million for that year.

Now let's pretend that there is a FairTax system in place. Arnold,
because he is crazy from years of steroid abuse, spends EVERY SINGLE
penny he earned, MC Hammer style:

30 million *0.23 = 6.9 million dollars paid in taxes, leaving him
broke. This is almost half of the amount of tax he would have paid last
year with the income tax. Who makes up for this 5.1 million dollar
deficit? The middle class? I don't know.

Let's go back to the income tax scenario, and this time let's pretend
that Arnold has a great tax guy who ends up getting his 40% income tax
down to 15%. Not a bad job. Arnold now pays:

30 million * 0.15 = 4.5 million dollars in taxes, leaving him with 25.5
million.

In order for Arnold to generate 4.5 million dollars with the FairTax
system, he would have to spend:

4.5 million / 0.23 = 19.6 million dollars. This crazy man would have to
spend about 20 of the 30 million dollars he made last year just to
equal the amount of tax he would have paid with an amazing tax guy.

More realistically, a guy like Arnold is going to spend, what, 5-10
MILLION dollars each year? That's only 1.15-2.3 million dollars in
taxes!

Now I'm not particularly interested in hearing about how the upper
class is overtaxed as it is. I want to see where the beef is in this
proposal. Where does the money come from? Let's look at another
example:

Guy makes $40,000 a year. This puts him in the 15% income tax bracket,
if I'm not mistaken:

40,000 * 0.15 = $6,000 in taxes. In order to generate that much money
in the FairTax system, he would have to spend:

6,000 / 0.23 = $26,100 of the $40,000 he makes.

But wait!!! The Fairtax system doesn't start charging taxes until you
spend ABOVE the poverty level! Since the average poverty level is
around $25,000, the man would have to spend:

26,100 + 25,000 = $51,100 which is more money than he earned!

Now let's pretend this same guy gets his $6,000 in income taxes cut
down to $3,000 by his tax guy:

3,000 / 0.23 = $13,000 he must spend + $25,000 (poverty spending
minimum) = $38,000 of the $40,000 he earned. So much for saving your
nest egg!

Here's the only thing I see going for this system, from the
government's perspective:

Let's say the guy earning $40,000 per year spends $24,300 normally. How
did I get to this number? I'll assume an out-of-college guy who pays
$1,200 a month in rent, $220 a month in his car payment, spends $400
each month on food+utilities, and throws in an extra $200 a month to
buy girlfriends presents, christmas time, etc. (yes I'm basically
describing myself)

After his $6,000 in taxes, he's left with 40 - 24.3 - 6 = $9,400 net
for the year.

Now let's pretend FairTax is in place: $40,000 - $24,300 in spending -
zero in taxes since I didn't spend above the poverty line = $15,700 net
for the year. So because of this wonderful system, I end up with $6,300
more dollars in my pocket. Let's say I spend every penny of that extra
money I've saved:

6,300 * 0.23 = $1,450 taxes to the government.

So even with all this extra money, going right back into the economy (a
good thing, I know) I still don't generate anything in taxes compared
to what I was generating before. Same thing goes for Arnold:

30 million - 15 million spent because he's crazy - (15 million * 0.23 =
3.45 million in taxes) = 11.55 million dollars net, instead of:
30 million - 15 million spent because he's crazy - (30 million *0.4
income tax = 12 million in taxes) = 3 million dollars net.

So the fairtax system saves arnold 11.55 - 3 = 8.55 million dollars. He
pumps it all back into the economy:

8.55 million * 0.23 = $1.9665 taxes to the government. So Uncle Sam
really ends up with 3 + 1.9665 = roughly $5 million from Arnold. I
still don't see where the other 7 million dollars comes from, to make
up for what he would have paid in income taxes.

Can someone a little more tax-savvy explain how this system will in
infact generate MORE tax revenue for the government, or just show how
it can break even? I DO understand how it will dramatically boost the
economy, but unless it makes us all multi-millionaires, we still won't
be spending enough, by my math.

.

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