Why shouldn't the burden be on the other side? Can you - can anyone - demonstrate that "close monitoring" actually makes it possible to prevent terrorism? That states will actually use it that way, when the threat of terror is so politically useful?
Because without making a strong case along those lines first, you can't even take the "I'll trade privacy for safety" position in good faith at all.
The 9/11 attackers were already subjects of surveillance when they attacked. The Boston Marathon bombers were already being closely monitored but were not stopped.
Disciplinarians, cops for example, have dreamed of omniscience since the dawn of time. The panopticon dates to the 1790s! Despite the fact that we come closer to a state of all-seeing every day, I'm not aware of any compelling evidence that it's actually turning out to be very useful to prevent violent crime or acts of terror.