Whether or not it actually happens remains to be seen. After all, no less that the FCC's Chairman Julius Genachowski said he has "urged Fox and Time Warner Cable to agree to a temporary extension of carriage if they do not come to terms on a new carriage agreement today." It could end up like TWC's dust-up with Viacom last year, which settled at the last second. Or it could be like DirecTV's negotiations with Versus, which resulted in Versus being shut down in September.
With all this going on, you might expect some enmity, and thus TWC has posted instructions on how to cut the cable, meaning how to head to Hulu, Fancast, or "any search engine" to find their shows. They can then use TWC's instructions (below) on how to connect your PC to a TV, and watch sans cable (TV, at least).
In a way this is like cutting off your nose to spite your face, as the horror that cable and satellite companies imagine is that people actually start doing this en masse. Companies like TWC and Comcast would still be needed for the Internet, but they might lose their TV subscriptions.
Naturally, not that many people would go this far, but it is something that some people actually have done, already. Through the use of Hulu or some other method (BitTorrent), they get everything via the Internet, one way or another.
Of course, there's always the one thing that will draw people back to TV: live sports and live events. Those are typically not broadcast as they happen. Anyone want to miss the Super Bowl?
As far as if this cut-off really happens, it looks like it will come down to the wire. The last major shutdown of major proportions came in 2004, when Viacom and Dish Network couldn't reach an accord, and a number of stations, including CBS, horrifically for CSI fans, were shut down for a few days.
Read the instructions below, as well as a video (not too professionally made, as there's some nasty coughing around 2:30).
Update: The two companies reached agreement Friday evening. The agreement, said to be "in principle," also includes the Bright House cable network.