I think the understandable public response is that drones or any other eye in the sky is another nail in the coffin of the Fourth Amendment, piercing the veneer of privacy. Like some other societies, our security isn't making us feel safer, it's making us feel like prisoners. The public is getting tired of being told that the War On Drugs justifies these measures and isn't quite willing to buy that they are essential for national security. The public wants to be able to swim naked in the back yard if it wants, without feeling like the government is watching.
If a drone lands in my yard, I am keeping it and selling it on ebay-slovenia.
This isn't about your feelings. Believe me when I say that nobody wants to see you swimming naked. The Fourth Amendment guarantees us the right to be secure in our persons, papers and homes. It does not provide an expectation of privacy in public, and the uses of these drones are going to be the same as the uses of other police aircraft, at least those uses which can be done without a crew. They will be used to track movements along the border, for example, to include drug smuggling and illegal immigration. They won't be used to peer over your backyard fence.