I live on the Gulf coast in Texas. It's hurricane territory. If the power is knocked out, the cable modem has no power, and in a few days the cell towers stop functioning. That's why we kept our land line phone.
You live on the gulf coast and don't have a backup generator? I live near Birmingham and have a UPS (for minor outages to keep some electronics running) and a small backup generator for longer outages (powers the refrigerator to keep food from spoiling and to charge the UPS). Our last power outage (the tornado that went from Tuscaloosa nearly to Georgia) lasted almost a day, but we had working wired broadband/vol-ip (u-verse) and cell service (sprint) the entire time (and didn't have to worry about food spoiling).
While our broadband comes over the phone lines, ours lines are mainly underground. We had many friends without a land line for a week because their above ground lines were ripped up by the tornado. Nothing is disaster proof - always have redundancy.