Is giving up privacy to gain security worth it?

Our privacy is something important. Allowing the U.S. Government to invade that privacy, guaranteed by the U.S. Constitution, in the name of security may have serious consequences:

Peggy Noonan: What We Lose if We Give Up Privacy - WSJ.com

She says, quoting Nat Hentoff, the great journalist and civil libertarian : If massive surveillance continues and grows, could it change the national character? "Yes, because it will change free speech."

Something worth considering? I think so. I don't believe I'm as willing to give up privacy to gain security as I used to be.