I don't get the impression that the average american cares very much about surveillance, whether it's by corporations or the government.

More than that I'd wager they'd be more likely to support it. As we've seen in the past just advertise it as a way to nab the most heinous form of criminals (terrorists, child predators, etc.) and enough people will be ok with it. Hell, even here, a site you'd expect to be strongly anti-surveileance, I've seen comments that basically equated to "I'm ok with [mass surveillance tech] because it's going to help stop [bad guy group]".