Per the speech transcript he clearly says "No-Fly" list. But the WhiteHouse.gov talking points refer to both.
Since Obama and his speechwriters were hazy about the relevant visa program under which a terrorist entered the country (darn these pesky details, when Obama has to fret about climate change in the 22nd century!), perhaps we can be excused for wondering whether they are also confused about this.
The explanation might be simple, although it means this "2,000 people" example is misleading. The No-Fly List is a subset of the broader terror Watchlist, and maybe the available reports cross-checking gun purchase applications doesn't immediately break down No-Fly listers as a separate category. Yes, that means the 2,000 figure may be wildly overstated, but this is Obamaville.
And do let note again the non-barking dog. Surely Team Obama has made an attempt to learn the subsequent criminal history of these people we are watching who are buying guns. I mean, we are watching them, yes?
So how has this history turned out? How many people have we been watching that bought guns and subsequently used them in ghastly crimes? Why isn't the White House trumpeting those examples of coulda-woulda-shoulda "Crimes prevented and lives saved" if this "common-sense" shredding of the Constitution had been adopted years ago?
People looking at it from the other end of the telescope have noted that many recent mass killers (e.g., Adam Lanza of Newton or Dylann Roof of Charleston) were not on a no-fly list and almost certainly would never have been considered for it.
Well. If I were a a trial lawyer I wouldn't ask this question - maybe Team Obama has an impressive list of criminals that moved from the watchlist to jail after buying guns legally and then committing crimes. But they ought to be waving that list in our faces, so their silence is telling.