It's not a tradeoff at all. Our intelligence agencies are likely the biggest threat to our security today. We are giving up liberty to be in more danger.
You are confusing privacy with liberty. While I view I have a right to a certain level of privacy, it has no effect on my liberty.
For example, if I were to strap a camera to my head and stream my life 24/7 onto the web, am I any less free than I was before? No, even though I had given up 100% of my privacy. My liberty would only be limited if I limited it myself. For example, if i decided not to view porn because the camera on my head would broadcast it and the whole world would know that I'm into midget-barbarian porn.
Liberty is diminished, however, when that lack of privacy is used against you. For example, if the state puts a GPS on your car and sends you a fine every time you exceeded the speed limit, your liberty would obviously be diminished. Or if the state put a camera in your bedroom and arrested you for masturbating in an unapproved manner.
Privacy is nothing more than the securing of information. Information has nothing to do with liberty. However, it could be used to restrict freedom.