In case you haven't seen this yet, the CBO has released a report showing that our tax system is, in fact, progressive.
This analysis rests on Table 1, where one sub-table assigns an "Effective Corporate Income Tax Rate" for each income group, by assigning all such corporate taxes proportionally to non-wage income. Since higher income groups have more non-wage income, they bear a disproportionate share of such taxes (40% of the entire tax burden for the top 0.01%).
That assignment only makes sense if you assume the economy to be uncompetitive. In an uncompetitive economy, a lower corporate tax would translate immediately into profits. In a competitive one, it seems that income tax is a corporate cost like any other, and that lowering the cost would lower prices, increase revenue, increase labor demand (and therefore wages), etc. I'm not sure how much of the tax should be assigned to each group (I can make a naive case that if 10% of corporate revenue is profit, 10% of the taxes should be assigned to owners, but don't have much confidence in it), but it's unreasonable to assign all of it to owners.
By assigning all the costs of corporate taxes to owners, the report is implicitly arguing that the economy is uncompetitive, and that raising corporate taxes would only affect the rich. This may be the first time I've heard conservatives make that argument.