[or you can ask them if they'd be willing to have a streaming camera installed in their bedroom]
I do, because it increases the power of an already too-powerful police force. America is the world leader in throwing people in prison, we really do not need to give the police any more tools.
That's the answer you'd get.
But yeah, until they see negative results, I doubt majority is going to start caring.
You can also put it in terms of hackers: maybe they have nothing to hide from the government, but what about from hackers? People seem to be more concerned about that sort of thing. The same technologies that would thwart the NSA also happen to be good at thwarting other attackers.
If you have nothing to lose, then you only have information to gain by invading others' privacy.