At least the 3G networks are still up for voice/sms fail-over.
Or a disgruntled employee left a cron job on all the key systems to rm -rf :-)
Here are some other wild guesses that may have little or no resemblance to what Verizon is experiencing, but kind of show what can bring down an Internet-like network:
* Some sort of configuration fat-finger that got rolled out everywhere without proper testing. You'd like to think that's impossible on this scale, but after having an insider's look at the operations of a couple major US cable companies, I put nothing past telecoms.
* Verizon probably runs some form of routing protocol internally. If a core router has gone insane, you could, conceivably, get route flapping and bring down pretty much everything, but that's not supposed to happen on carrier-grade equipment (cough see previous paragraph).
* In a closely related scenario, large portions of the public Internet have been brought to their knees at least once by a nasty BGP bug in a major vendor's routers that got triggered when somebody broadcast just the right set of options in their announcement. Picture a guy in upstate New York trying to route around a bad line card, and suddenly the US goes dark because half the routers crash when they got the BGP table update.
You can probably spot a common theme here -- a "decentralized" but homogenous network is still vulnerable to the triggering of problems shared by all points.
So even though LTE is ostensibly an IP-based system, there are a host of dependencies on single vendor closed management systems and protocols that could be the cause of any outage. A nationwide outage points to the failure of one of these systems to properly handle letting subscriber stations onto the network, not something simple like getting packets from here to there.
Think failure of the RADIUS/DNS like systems, not the routing infrastructure.