They're nominally "not ok" with it, unless it's couched in some piece of legislation like the PATRIOT Act or snuck into a Defense Authorization Act, particularly after a national tragedy happens. Then a lot (a majority?) of Americans will suddenly be ok with the "if you got nothing to hide you got nothing to fear" mantra.

I'm actually not a huge fan when people act like Americans are a a bunch of flag-waving morons, because I think that people who say that are often being extremely reductive to a borderline-offensive level [1], but in this case I do think Americans are uniquely ok with pretending their rights don't exist when they're convinced it's for a greater good.

[1] Disclosure, I'm American