Now, I wouldn't read too much into it (and John Sides cites other polling with different wording that shows the opposite results). John has it just about right:
It's a fool's errand to try to generalize about the ideological proclivities of the American public -- right, center-right, center-left, etc. The most salient fact is that most Americans don't have political ideologies similar to those of many political elites. Instead, their attitudes toward something like the role of government are more often ambivalent.What polls like this (at least combined with election results over time in which mainstream liberal Democrats do just fine) do show that it doesn't seem to matter very much that Americans like to call themselves conservative, and especially that they don't like to call themselves liberal. Really -- suppose that Sara Robinson spent her requested $100M and, presto!, it worked: instead of liberals running away from that label, they wore it proudly, because all the people who currently believe things liberals believe and/or vote for liberal candidates now thought of themselves as liberals. What would change? Well, nothing that I can see. Oh, some superficial things would change, perhaps. But it wouldn't create a market for liberal candidates pushing the idea that government should take responsibility for this or that pressing issue, because as the polling tells us that market already exists. On the other hand, it also wouldn't destroy the market for conservative pols. Indeed, people would still, just as they do now, manage to hold completely conflicting ideas about what government should and should not do. Why shouldn't they? Most of us never have to resolve conflicting impulses about individualism and the community, or about government that should guarantee the basics of life and government that reaches too far into our lives. Both sides have long cultural histories, and therefore make intuitive sense to lots of Americans when seen through the right lens. And building up liberalism or progressivism as a "brand" isn't going to change any of that.