There is AUVSI http://www.auvsi.org/auvsi/home/ (Association for Unmanned Vehicle Systems International). I don't exactly know how effective they are what they do or even what they do, for that matter. They do seem to come up a lot in these drone issues, but their Wikipedia page appears to be self-written.
There may need to be something more than that; a "drone lobby" perhaps?
The AUVSI is known for generally representing more of the traditional military-industrial side of the drone business than the smaller, more entrepreneurial side. E.g. see their corporate membership list, which includes Boeing, General Atomics, Lockheed, Northrup Grumman, Rockwell & Saab (along with newer members like Google & Amazon) at the "Diamond Level": http://www.auvsi.org/membershipandchapters/corporatemembers
The Silicon Valley chapter of the AUVSI is more progressive with regard to small business drone advocacy, but it's hard to tell if that is having an impact nationally.
I could imagine license tags being one outcome of this process: If a drone goes spying outside your window or damages your property, you now have a fairly simple recourse of reporting that tag number. The existence of this recourse would also go a long way toward making civil drone use less scary and more socially acceptable.