There's a huge difference between this claim and lawful intercept on demand -- meaning that a formal request is made to the Telco to intercept such and such number for a period of time, then the calls are re-routed to special recording equipment.
In this case you'd need to have active real-time recording capability for every call made on every switch in the entire national phone network. You'd also have to hide this capability from the techs who work on the switches and/or swear them all to secrecy. That would be tens of thousands of switches, and many thousands of technicians.
Leaving aside the fact that you'd have to re-engineer the switches themselves, since they were not designed to support this kind of logging (no storage capacity, limited CPU, etc.)
All it would take at this point is a single wagging tongue or a Wikileaks dump to break the whole thing open. Since we've seen this happen for much smaller wiretapping deployments, I'm skeptical that you could pull anything like it off without everybody knowing.
What you can do is monitor trunk lines (which is what happened in the case of the Folsom Street tap, mentioned above) and you can certainly build your own wireless interception hardware. But this is a very different thing than what TFA claims.