Who watches the watchmen?
Any organized government is going to draw people who watch them right back - those people might use their time to notify those under watch that they are being watched. There's a lot fewer people that are professionally paid to watch others than there are people out there with spare time on their hands. Given the level of distrust of our government, I can imagine a lot of people taking it in their own hands to be watching the watchmen right back... Even going so far as to arrange groups that take rotating shifts and provide instant notifications.
When somebody asks you to trade your freedoms for security, it isn't your security they're talking about.