That is what it usually comes down to. We can have a privacy intrusions and a greater safety, like the ability to outset the terrorist attack. Or we can have our privacy and give the government harder time, to stop attacks like that.
I value the privacy more than my safety, but I can never tell if my opinion is a minority or the majority. I would prefer to have my privacy and not have some government official look over all my life with a couple of keystrokes.
Even if that means, that someday I am going to find my death in some violent attack.
Let's look at the statistic. The most common killer in the western world is not even human. They are illnesses like heart disease, obesity, and similar side effects of what is considered the normal life style in the western world.
Only in USA, the number of people dying from texting while driving is twice the amount than the number of people dying in 9/11. And that is still considered one of the biggest terrorist attacks. Hell, hippos kill almost as many people in Africa each year, than the number of people dying in 9/11.
So even if the government stops every single terrorist attack that can happen, that still won't lower the amount of total deaths in the world. No matter how good the computers get in predicting and how much information they gather, we are still far away from preventing every death.
There are going to be at least decades, before we are that good, to be able to predict accidents. And I doubt that there is a way of preventing people stupidity, without brainwashing them.
So no matter how much information does the government gather, they will not make our life really that much safer. But it can increase the feeling of being safer, and some people might value that. I just do not know, if pulling the wool over the eyes of the people is really such a good idea.