I think one good response to "I have nothing to hide" is that everyone has facts about them that could be misused by parties with bad intentions.
Perhaps commenters could suggest some other good replies.
Perhaps commenters could suggest some other good replies.
Or SSN, etc. Sort of an identity theft angle.
Or "And do you have Facebook? GMail? I'll need those too. You've got nothing to hide, right?"
It's a bit of a flimsy argument but it still makes people think.
Usually they won't give this sort of information to a random person because they're not "The Government". Of course, "The Government" is just made up of regular people, who have their own personal beliefs/motives/etc.
Plus agencies don't have a stellar history of keeping our information secure (OPM hack, etc.).