Social security has held up very well over the decades, despite forecasts to the contrary. The people who set it up predicted back then population and demographic models that were within 0.2% of actuals into the late 80s at least. So they definitely knew what they were doing and did their math. Social security took a hit when the benefit payouts became inflation indexed, but that was mostly adjusted for.
Remember that the timelines Bush is quoting are the absolute worste case scenario as predicted by the state actuaries. They come up with basically 3 estimates every year, and their middle pick was typically right on, until a few years ago when they became a little pessimistic (no, no agenda there) and their optimistic estimates are now closer to reality. If you follow the historical line of predictions vs reality, a small bump to taxes will cary social security through the tough years until the baby boomers start dying off (if you'll pardon the crassness). But really, no one can predict with certainty that far into the future, so Bush can say whatever he wants and no one can prove othewise.
When you try to fix social security by privitizing it (just call it what it is), you're removing a) the social aspect (it's now individual) and b) the security aspect (money's tied up in stock market, weee!). It frames Social Security in terms of an investement, when it is really insurance. Insurance removes risk, by pooling it and spreading it over time, stock market investement increases it. The idea here is that even though many (most?) individual investors will make money over 30-40 years, many will make very little and some will lose their shirt. That's where social security steps in, to provide a baseline living allowance if you couldn't hack it (although lack of means testing makes that a bit of a farce).
Ah, screw it, they should just go all the way and get rid of it altogether. But no, the money will be directed to a select few funds, indexes and some other instruments, maybe bonds. While that does not favour any company explicitely, indexes are composed of a few large companies. Billions will pour into them overnight, and no one knows what that will do, aside from the obvious. And someone will make a nice commission off the whole deal. Also, index fund does not equal diversity. Just look at the composites. Indexes don't have fundamentals, they're as likely to go up as down. And as always with the stock market, tough luck to you if you need to cash out at the wrong time! (With so much mindless money pouring in left and right, it's pretty safe to assume stock swings will be even wilder and more unpredictable.)
Instead of directing investement to their pet benefactors, the government should just let people do whatever they want with it. I bet what you would see in short order is a private version of Social Security, basically insurance (pooled risk) which is what social security mostly is. But instead of insurance (or assurance) for your non-productive years, all you will get is insecurity and a gamble, and big companies will have the windfall. This is a halfway measure which is totally inappropriate for backing baseline insurance.
<=---- someone should make a smiley version of this!