There is a chart at the bottom of the article I linked that ranks different institutions about which people were all asked the same question "How much confidence you you have in institution X". Note if you include the "some" answer, the "generally positive responses" tally rises to 83%, with only 17% saying "very little" or "none".

But more importantly, the police were the 3rd highest rated institution, behind "small business" and "the military". They ranked above "higher education", "the church or organized religion", "public schools", "organized labor", "banks" and "newspapers".