TGGP was so right in the last post to ask, "Where's the data?"
GSS respondents were asked the following question: "Some people think that the income differences between the rich and the poor ought to be reduced, perhaps by raising the taxes of wealthy families or by giving income assistance to the poor. Others think that the government should not concern itself with reducing this income difference between the rich and the poor. Here is a card with a scale from 1 to 7. Think of a score of 1 as meaning that the government ought to reduce the income differences between rich and poor, and a score of 7 meaning that the government should not concern itself with reducing income differences. What score between 1 and 7 comes closest to the way you feel?"
Unfortunately, the question is double-barrelled, asking about taxing the rich and helping the poor, but if anything, the wording should tilt responses toward government intervention.
I divided the sample of whites from surveys from the past decade into three equally sized groups: low-income, middle-income, and high income. The mean responses to the question look like this:
The low- and middle-income groups are significantly more in favor of equalizing, but the differences are fairly small (Cohen's d for the low/high comparison is .32).
Plus, the typical response for the poorest group is close to 4, which is the neutral answer. Even poor whites are pretty indifferent about reducing inequality. I don't see stick-it-to-the-rich sentiment here.