From Hear the Issues (a site I'm not familiar with, so I don't know if it has any angle):
A Gallup poll released on June 21st, 2005 shows that Americans' confidence in the Supreme Court has been declining. Gallup asked Americans to rate their level of confidence in 15 institutions in American society, including the Supreme Court. The Supreme Court ranks in the middle of the list, much lower than the military, police, and organized religion, but higher than HMOs, big business, Congress, and organized labor.
Overall, 4 in 10 Americans say they have a great deal (16%) or quite a lot (25%) of confidence in the court. This 41% confidence rating is among the lowest Gallup has ever found for this institution, and it perpetuates a gradual decline in the public's confidence over the past three years.
The story also reports that traditionally Republicans have had greater confidence in the Supreme Court than Democrats ("Republicans and Democrats were not radically different in their confidence with the court from 1973 until 1984, at which point 57% of Republicans and only 44% of Democrats said they were confident in the court."), but that confidence by conservatives has fallen during the past three years, in part because of popularity bump for the Court with conservatives after the 2000 election (or as the article puts it "after the court decision that gave Bush the presidency").
The public's current confidence rating in the U.S. Supreme Court is among the lowest that Gallup has found historically. Republicans and Democrats currently show only modest differences in their views of the court -- a much different picture from what Gallup found after the 2000 election controversy when Republicans were much more likely than Democrats to express confidence. Conservatives, moderates, and liberals have roughly the same level of confidence in the court, but since 2000, ratings of the court among conservatives have dropped significantly.
I tried to click through to the Gallup Poll itself to get the primary sources, but this poll seems to be subscriber-only.