A millionaire's view on inequality and taxes, however, seems to depend more on their politics than their wealth. Eighty-six percent of Democratic millionaires said inequality is a problem, compared with only 20 percent of Republicans. Two-thirds of Republicans vs. a quarter of Democrats say anyone can become wealthy in America if they work hard.
Democratic millionaires are far more supportive of taxing the rich and raising the minimum wage. Among those who say inequality is a problem, 78 percent of Democrats support higher taxes on the wealthy, and 77 percent back a higher minimum wage. That compares with 31 percent and 38 percent, respectively, for Republicans.
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Politics even plays a role in how millionaires view wealth creation. Among Republican millionaires, 63 percent say hard work is the No. 1 reason the wealthy are wealthy. Democrats were most likely (45 percent) to cite a person's family or place of birth as the top reason for their wealth.
The bottom line: American millionaires, in general, agree that inequality is a problem. But when it comes to solutions, millionaires are just as split along political lines as the rest of the country.
—By CNBC's Robert Frank