1) High income and high wealth are not the same thing. People keep mixing the two together (switching between "tax high incomes" and "tax the wealthy" like they're the same thing).
2) Many rich people don't have huge piles of money lying around, but instead own valuable companies or other assets. For example, Mark Zuckerberg owns a large part of Facebook, but that's not directly convertible into its equivalent in dollars. In fact, after the IPO, he had to pay an enormous amount of taxes on that, which was money he didn't have at the time [1].
1 - http://www.forbes.com/sites/robertwood/2013/12/20/mark-zucke...
He got that tax bill by exercising his options--he bought shares at $.06 that were worth significantly more, thus giving him a great deal of taxable income. It was in the form of shares, but it was still income. To say he didn't have the money at the time is a bit dishonest--those shares were (and are) highly liquid.
Are they? If he tries to sell all of them, will he get exactly what they're valued at? Selling a quantity like that will probably pull the price down significantly.
This is all guesswork though. Anyone here more knowledgeable that can jump in?
On the day of Facebook's initial public offering, Zuckerberg exercised a stock option and purchased 60 million Facebook shares at a "strike price" of 6 cents each. Even if those shares are never sold, the IRS treats them as ordinary income at the time the options are exercised. The rationale is that such options are a form of compensation, just like regular wages.
1 - http://money.cnn.com/2013/03/28/technology/zuckerberg-tax-bi...