To the best of my knowledge, most of the techniques Obama uses do not have names. So I'll make up some names as I go through a few examples.
Adopting the premise. It's farily common among public figures to take a fact or an entire argument from the other side and simply state it confidently as if it supported your own conclusion. Done right, it makes your audience believe that you have more support for your position than you really do. But more importantly, it disarms your opposition.
In this case, Obama points out a few facts about the surveillance: (1) that it's been authorized by the Congress, (2) that it's been renewed several times, and (3) that it's been going on for a long time. Of course, one could argue (and I think, should argue) that the authorization by Congress wasn't meaningful, but let's grant the point. In any sane discussion, it would be pointed out by privacy advocates, not Obama, that (1) and (2) are the worst aspects of the entire program. If it had been discovered that this surveillance was the work of a rogue band of overzealous NSA employees, there would be no problem. It would simply be shut down and the people responsible would be held accountable. An official, properly authorized invasion of privacy is far worse than an illegal, unauthorized invasion of privacy. But Obama treats this as if it were support for his position, when in fact, very few people are alleging that the programs weren't authorized.
A clearer example of (what I'm calling) "adopting the premise", is the last point -- that it's been going on for a long time. An invasion of privacy that's been going on for a long time is far worse than one that's just started, for the simple reason that a lot of damage has already been done. In a sane discussion of these issues, privacy advocates -- not the President -- would be the ones pointing out that this program has been operational for years. But by adopting this premise, Obama effectively removes it from the discussion.
Value adoption. Audiences (including readers) make factual judgments based on the values that the speaker (or writer) professes. For example, if you're a self-professed "compassionate conservative", a lot of people will assume that you won't cut aid to families with small children. "Value adoption" is the technique of professing (directly or indirectly) the values that motivate your opposition's argument. People will assume that you're like them, and therefore that the actions you take will mirror their values.
Obama clearly deploys this technique when he forcefully says, "I welcome this debate, and I think it's healthy for our democracy." If someone truly believed in openness and transparency in government, this is exactly what they'd say. Obama's assertion that the debate is "healthy for our democracy" draws on the precisely these values, in addition to ideals about the democratic process.
If "value adoption" were in the critical reasoning textbooks, this would be a textbook example of it. Obama actually believes precisely the opposite. Obviously, the programs have been kept secret for years, despite the fact that Obama could have declasified them at any time. Furthermore, everyone in the administration is loudly claiming that this very discussion is harmful to our democracy, because it (allegedly) puts the nation in danger. In a sane discussion, privacy advocates would be the ones saying that the discussion is healthy for our democracy because their actual values would place the discussion above whatever damage (if any) is done to our security.
Reverse equivocation. An "equivocation", in the ordinary sense, is when one word is used to mean two different things in the same argument. A "reverse equivocation" is when two words are used to mean the same thing in the same argument.
This is usually harmless. But if deployed by someone as intelligent as Obama, it can be very powerful. He does this when he shifts from referring to the "FISA court" to the generic term, "federal judges". The FISA court is the group of federal judges that authorizes a large part of the surveillance conducted by our intelligence agencies. These judges are appointed by the Chief Justice of the Supreme Court for a term of service, and they are drawn from other federal courts.
Obama refers to the FISA court by name very sparingly, presumably because it exeplifies practically everything that privacy advocates dislike. He only uses the term twice by my count, and only passively, as in, "This program is fully overseen, not just by Congress, but by the FISA court". After that, every single time he refers to the FISA court, he avoids using that term. Instead, he refers to "federal judges", and he does this without exception. For example, he says that if anyone in government wants to conduct more intrusive surveillance, "they'd have to go back to a federal judge" to get authorization. He also says that "federal judges are overseeing the entire program".
Reverse equivocation can be technically truthful. These people are, in fact, federal judges. But these are not ordinary federal judges, and this is not an ordinary court. However, when Obama generically refers to "federal judges", we think of real courtrooms where there are lawyers arguing for opposing viewpoints, established case law, an appeals process, and a public record. None of these are true of the FISA court. Only one side is argued, the court's decisions are kept secret, and its decisions are creating case law that's independent of what happens in the broader legal world. And we have no way of discovering what that case law has evolved into.
Obama has created a growing library of masterful rhetoric. Let's try to learn from it.