(Read more: Zuckerberg to sell $2.3 billion worth of Facebook shares)
A $2 billion payment this year would be around 4 percent of the total income taxes that were collected in California in 2012.
It's hard to say whether his tax bill is the biggest this year—or ever—because the IRS doesn't rank the top taxpayers. And while Forbes, Bloomberg and others track the wealth gains of the rich, no one tracks the top taxpayers among the rich.
The IRS does crunch data on the top 400 earners each year. For 2009, the most recent period available, the top 400 earners paid a total of $16 billion in taxes, with an average tax bill of $40 million each.
Zuckerberg's tax bill could be more than 50 times that amount.
Of course, his tax bill is so high because his income (at least on paper) is even more massive. And with a net worth of more than $27 billion, according to the Bloomberg Billionaires Index, it won't exactly cramp his lifestyle. What's more, Zuckerberg has charitable deductions and trust structures that help reduce his effective tax rate.
(Read more: Just how fast are the rich becoming richer?)
But Zuckerberg is an extreme example of a dangerous phenomenon: the stock sales of the wealthy account for an outsized share of America's income taxes. And that dependence is growing with a rising stock market and a growing income gap.
In California, the top 1 percent pay more than 40 percent of the state's income taxes. The stock-selling, super rich like Zuckerberg account for a large share of that 40 percent.
Facebook's initial public offering was so important to the state government's tax collections that it had to lower its budget projections by more than $600 million because of the company's weak IPO. Now that Facebook's shares are soaring, the budget probably needs to be updated with higher revenue numbers.
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For now, Washington and Sacramento are cheering the soaring stock market, and sellers like Zuckerberg. They won't be as happy when the trend reverses.
—By CNBC's Robert Frank. Follow him on Twitter