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Mostly what you are hearing in the treatment of Romney's voice is added reverb. The way it's used in the ad, it creates the sense that Romney's voice is echoing inside a large empty space (like a closed down factory). In the context of the ad, it creates a very powerful effect because it enhances the sense that these once thriving places of business are now vacant of people (rooms are much more reverberant when empty).
It sounds to me like there has been some additional audio editing, because the character of Romney's voice shifts slightly each time the scene in the visuals changes. This would have been done with frequency equalization (EQ), many digital audio editing programs have preset EQ curves designed to mimic certain kinds of effects (old time radio, etc.). The tinny quality you notice is a result of filtering out the lower frequencies of the sound spectrum.
Obama's ad team has come up with a very effective juxtaposition of sound and image in this ad. I have a PhD in Cinema Studies and one of the topics that I studied very seriously was the way in which sound can effect how we perceive images, making them more powerful in our minds. At the risk of stating the obvious, this ad was put together very carefully by people who really know what they are doing. There is much more than just good political messaging going on in this ad. This is one for the history books. In my opinion, people will be talking about this ad for years to come.
I think you are on target to make a connection to LBJ's "Daisy" ad. The filmmakers used reverb pretty aggressively on the male voice that picks up the countdown, which added to the sense of foreboding. I'd have to do a much closer analysis of both ads to say much more, but "Daisy" came to my mind immediately upon seeing this ad as well.