The traditional method of oversight is via congressional committees and the court system. But even if you assume that intelligence organizations are reporting their activities honestly, those don't really work anymore. Once a program is in place, courts end up rubber stamping virtually every application and congressional committees do pretty much the same. They simply become too accustomed to what's going on to truly pay attention. And in the case of Congress, even if some members do have issues, they're all but gagged from speaking out about them.Congress is gagged, yes -- but because they allow themselves to be gagged. It's not inherently up to the bureaucracy or the president to set the rules about secrecy. Congress can do that. And they do, either explicitly or implicitly.
Granted: both the president and the bureaucracy can fight for the rules they prefer, too. But Congress, when they really want to do something, have plenty of tools to make it happen.
The reality here is that Members of Congress, with only a few exceptions, have been perfectly happy to gag themselves. To some extent that's because they approved of policies they didn't want publicity about, perhaps because they believe publicity would harm the consensus for those policies. To some extent it probably is because they are concerned about actual national security damage if secrets were publicized; that can be sincere even if it's wrong. But to a large extent, it's probably because pretending that they have no ability to do anything -- they can't even talk about it! -- is a very nice way of ducking responsibility.
I wrote something over the weekend saying that those upset about the NSA stories should be putting a lot of the blame on Congress, and this is yet another part of it. This is Congress's job. no one should let them off the hook with the excuse that they "have to" do what the NSA or the president says.