Gallup reports here that public confidence in the Supreme Court is at its highest point in four years. (Gallup's content is typically free to nonsubscribers on the day of release only.) The trend graph is kind of interesting. Bush v. Gore, which gets political junkies all excited, was apparently a minor blip on the radar screen for the public at large, with only a small drop in January 2001 from the previous Labor Day. The big slide in public confidence came in 2003-2005, from which the high court has apparently recovered. Gallup analyst Jeffrey Jones suggests Lawrence v. Texas, Kelo v. New London, and McCreary Co. v. ACLU as the reasons for the slide.
The number of people who think the Court is too conservative now significantly exceeds the number who thinks it's too liberal for the first time in the 13 year history of that question, but the Goldilocks position is still the plurality choice.
Although the Justices don't stand for election, public confidence still matters to an institution that has no direct power and depends entirely on public respect for its orders to be carried out. Only two Presidents in American history have defied the Court. You probably have portraits of one or both in your wallet.