This is, of course, a question that will be answered differently depending on the political and other opinions of the person answering.
My own view is that there is something of a sliding scale here. The answer is not always the same. The more that national security is truly endangered, the more important it is.
In an answer to a previous question of yours, I said that terrorism is not an existential threat to the US and that, therefore, privacy is more important. But if the US were more threatened by terrorism, the answer might well be different. Think about Israel during the "intifada" or Northern Ireland during "The Troubles." In those cases where terrorism was a clear and present danger to practically every person every day, privacy concerns would probably not trump security.
Overall, then, I would argue that privacy trumps security in places that are relatively secure but that security is more important in more dangerous places.