With all due respect, it is sort of a circular argument to say that Verizon doesn't care about marketing the Nexus because most people don't know about the phone, when it is also true that the reason most people don't know about the phone is the lack of marketing from Verizon.
I agree with you that most people never heard about the Nexus. Then again, I'd bet a good chunk of people don't know the difference between 3G and 4G, or what a 720p display is, but that doesn't stop Verizon from advertising these things because they are selling points. The responsibility of a marketing department is to convince customers they want a particular product by setting out its selling points. The Nexus would be an easy product to promote even to the lay-person (how about largest screen, 4G, revolutionary operating system for starters?) and the fact that Verizon hasn't promoted it at all is really shocking to me.
EDIT: I am aware that Verizon could still advertise this phone after release, but I think it is crazy to not hype a phone that is coming out so close to Christmas, only to turn around and hype it after people have already done their Christmas shopping. Also, I don't know why Google or Samsung haven't stepped up with advertising dollars either.