You sort of glossed over the thrust of my argument in one sentence. We don't just throw people in jail (mostly). They have to be charged, and go to court, and be convicted by a jury, etc. Due process. It's not like we systematically disappear people because they were overheard saying something about the President. Stating that they do not enjoy such protections does not make it so.
They *do* have to get a warrant for targeted surveillance. They get it from FISA.
What I'm not okay with is then monitoring the other individuals that use these devices or connections when those individuals use other devices or connections, without first obtaining warrants against those individuals as well.
That's never going to happen. Even if the scope of the warrant was limited to, say, the owner of the line, courts have repeatedly and consistently permitted information acquired incidental to the execution of the warrant. That is to say, if there's a warrant to search your house for documents, and they find your husband's drug stash while executing the warrant, they can still bring charges against your husband. So the scope of the warrant might be limited to the owner of the phone line, but in reality, they would have to listen to the conversation to know who is speaking, and in so doing they may make additional, admissible, discoveries.