I hope what you say is true, but my experience and information tell me otherwise.
I've been doing talks at meetings on the budget and Social Security. The people who tend to proliferate at these things are middle- to upper-middle class elderly folks, clearly not a representative sample. The idea of private accounts is appealing to them and I suspect to many others. They don't do the calculations necessary to compare options. The reasoning is pretty simple: the system is in some kind of trouble (everybody says so); benefits are low, relative to the standard of living to which we would all like to become accustomed; stock market returns are usually higher, especially now; ergo, privatization is a good deal.
I don't know what polls you're referring to re: young people. The ones I hear about are those which reflect uncertainty about the system, not confidence. As I said, I hope you're right.
I meet with people who work on the politics of this and nobody has found any support for tax increases yet (except when you force people to choose among less appealing alternatives). The problem of course is that people don't realize that tax increases are the least bad option. If they knew that, we wouldn't be in the current political situation we are.