Here's a broad list of consequences that is by no means exhaustive:
1. You can be indicted and charged with a number of felonies, most notably treason and violating national security, for your private correspondence and electronic habits.
2. Incidental to an existing charge, you can have your private interests and communications leveraged against you as evidence not directly relevant to what you're being tried for.
3. You can be implicated in crimes for communicating with known criminals or having any demonstrable (reasonable or otherwise) association with "people of interest." Corollary to this, you could be harassed and pursued and made to act against such people in the interests of national security.
4. You could be blackmailed or slandered in the public eye, effecticely crucifying you in the media, by taking your private life out of context in the name of the legal process.
5. You would be effectively "nude" in the virtual sense - every thing you do is and could be an actionable offense or interpreted as one, despite the fact that it's not in direct offense to anyone else and despite the fact that it's private. Your every interest, hobby and habit could be dissected and questioned as though an Orwellian thought police agent were ever vigilant in your room.
6. Innocent until proven guilty would be effectively null and void. You could be presumed guilty for all of the aforementioned reasons and due process would be extremely hard for the average individual to utilize to their advantage.
All of these would scale (against you) in a situation involving mass media. You might believe that on a cursory inspection these are justified if it prevents terrorism. That is a fear response, to which I reply that our government, and the rule of law it represents, is lost if we walk down this path.
Sacrificing liberty for the sake of liberty is both absurd and fundamentally objectionable.