"@TheGhostmaker: "That's because everyone knows that free markets work, but in practice everyone responds better to suggestions that are not free market." That is true... but in what sense? I suggest that people's feeling that "free markets work" is mostly because they have had that drilled into them all their lives... it is "common sense" - right up there with "we live in the best country in the world"... it is a feeling more than a well supported thought. When you actually define what a free market is people give a more nuanced view."
Perhaps, and what you say is a valid interpretation of the results (clearly you can read either way) but I think that in fact looking at the specific case can remove the clarity of the original arguments. You become increasingly open two a few errors of reasoning:
1. "Something must be done". If anything gets discussed in politics, doing nothing stops being an option that people consider, particularly politicians. In a free market approach, you are doing nothing most of the time.
2. Nirvana fallacy. People compare the imperfect solution of the free market (necessarily imperfect) with an idealistic view of government. The issue is that with government regulation and support programs, there will be errors made as well.
3. Ignoring special interests. A kind of Nirvana fallacy, in a way. People stop remembering that even if a good solution is possible in government, there is the inherent risk of a good program being worsened by the actions encouraged in the political process, which are not necessarily beneficial.
4. Ignoring unintended consequences. It is very hard to credibly identify unintended consequences, but they certainly exist. Often the claims appear silly, but prove true (e.g. seatbelt laws increasing number of accidents)
5. Nobody can be missed. It is often wrong to claim that nobody in the whole of society can be allowed to suffer something. Normally making this claim requires programs costing much more than what is being provided for, since it is commonly prohibitively expensive to identify the final few who are in need, and prohibitively expensive to provide for everyone.
This by no means sum to an argument against all government action in the economy (though the public choice theory ones could be expanded to perhaps argue that point), but they do I think justify why people are more right wing in the abstract than in practice.