By statue, the NSA can't actually do that. The mass unwarranted surveillance of phone conversations was a short-term program that was ultimately shut down as soon it's existence became known outside the Oval Office. Even Bush's Attorney General said he couldn't do it. The bulk collection of telephone metadata lasted for maybe 15 years but was ultimately allowed to expire due to both ethical concerns and because it didn't yield a lot of value.
The NSA is primarily tasked with overseas collection. IE tapping Osama bin Laden's satellite phone. And they report up the chain to the DoD. Meaning they aren't even looking for domestic criminals and may not notice if they surveilled one. If they're doing anything beyond their legal parameters or beyond their remit, they wouldn't broadcast it or expose themselves by using it to arrest someone.
I like to point to the Gestapo as a counterexample. They are the archetype for police state surveillance. And they did it in a country where most people didn't have even a rotary phone let alone the internet. The distinction between a police state and a free society is entirely up to will and not technology.