nnnnnot quite, they have the capability, MAYBE, to monitor a couple hundred people intensively at a time, or a central repository with many people interacting, but let's make very clear the government is not and cannot monitor 'everyone' on this astronomically huge global network. They do apply very broad patterns to sniff up on large SONET (fiber optic long-haul) networks between large metro areas, but they will never have enough resources to monitor us all. On the large pipes all they can do is hope to pick up a few keys words in series. Even more comforting than their woefully finite resources, we have access to strong crypto so with intense preparation we could almost vanish completely.
There are ways of keeping DB online should they mess with the continental links under their jurisdiction. It's mega-easy to get a foreign Point of Contact and server and start from scratch.
This network is the wild west and due to the underlying protocol limitations, it will stay that way for a very long time.
Surf prudent but surf free