I'm not sure why the inconsistency noted by Diane between the Findlaw and Rasmussen poll favors the Findlaw results. It could be that Rasmussen is right and Findlaw is wrong. A possible (partial) explanation for the inconsistency: Findlaw polls "American adults," while Rasmussen polls "likely voters." Typically, 40 percent to 50 percent of eligible voters vote in presidential elections; if "likely voters" is a subset of eligible voters, and both are more informed than "American adults" in general, then we might conclude that Rasmussen surveyed people who are more likely to be knowledgeable about public affairs, including the identities of Supreme Court justices. The puzzle, then, is why, within this subset of Americans with more information, people have favorable attitudes about the court and unfavorable attitudes about the individual justices. (The Rasmussen results also suggest, consistent with Findlaw, that substantial numbers of likely voters don't know or have no opinion, of course; but that doesn't address the puzzle, either.) I do not understand how the relative invisibility of the justices on the court explains the attitudes of those who do in fact see them.
However, I like Dahlia's hypothesis : Americans believe that the court has a valuable institutional role, but they resent the fact that these nine people exercise so much power over them. The more that these individuals have distinct personalities, flaws, quirks, recognizable ambitions, and so forth — the more they seem like ordinary human beings rather than disembodied spirits — the more difficult it is to acknowledge their exalted status in a democracy where authority is supposed to flow from the people. Perhaps judges, like priests, receive power on the condition that they withdraw from the world and submerge their identities in a public institution, and people sense and resent that some of the justices are violating their side of the bargain. Why didn't the oracle at Delphi write her memoirs or a how-to-be-a-supplicant book? Perhaps she better understood the political psychology of her position? An ironic twist: Are the justices who have made themselves more publicly accessible driven by democratic instincts that are inconsistent with the premises of their office?