I would echo everything that Will has said here. I don't have as personal an example, but reading your post idaho, I immediately thought of Cst's Ross, Gevaudan and Larche of the RCMP. They were tragically gunned down in Moncton, NB on June 4, 2014.
Despite a few pretty rough years PR-wise for the RCMP, when the news hit the whole nation felt gut-punched. I live on the opposite coast and people here were reeling. The outpouring of love and support actually chokes me up even now as I write about it.
Idaho, I've not been where you've been, seen what you've seen nor done what you've done. That said, I still believe in my core that, deep down, the average, decent person supports the police. He may bitch about the ticket he got or the latest news story but deep down he knows that without the sheepdogs who go out into the dark to push back the ugliness, the violence and the chaos for a just a little longer, life would be unliveable. It's dirty, dangerous, thankless work much of the time. Nonetheless, when push comes to shoot, the overwhelming majority of people still know who has their backs.
"People sleep peaceably in their beds at night only because rough men stand ready to do violence on their behalf."
Stay strong and be safe, brother.