Probably because the repeating stations, which receive the cell phone signals and retransmit them (you know, those big metal towers with antennas that have been sprouting like mad all over town? There's one 300 meters from my place) don't have any power.
Turns out that is *exactly* what it is. My dad heard on the radio in Paducah that AT&T is trucking in a fleet of generators to get their repeating stations in the area running again.
In the meantime, even my two brothers who aren't in Paducah can't get incoming calls since their Paducah numbers cause their incoming calls to be routed to those dead repeating stations. They can call out most of the time, though.