In the event of an emergency or a disaster the phone systems will almost certainly be overwhelmed. In Washington state we had a relatively minor disaster on May 23, 2013. At approximately 7pm an oversided truck drove onto a metal bridge on I-5 that spanned the Skagit River. The truck box struck the bridge trusses causing the bridge to collapse into the river (details). No one was killed but two cars fell into the river.
This event caused lots of damage and created a severe traffic disruption. However, on the grand scale of possible disasters it is a relatively minor one. Imagine if a severe earthquake has cause multiple bridge failures and structural damage to dozens or hundreds of buildings. In spite of the relatively minor nature of this disaster the phone service in the area was completely overwhelmed. Calls could not be completed and some of the overloaded phone systems crashed.
In a more severe disaster the phone system will either be completely down or completely overwhelmed. The 800 MHz radio systems used by emergency responders will also be overwhelmed. In a disaster you will probably NOT be able to communicate locally. You may be able to communicate out of the area using a hard LAN line phone. In a disaster use your mobile phone ONLY for emergency calls since MANY other people will be competing for the limited phone resources. If you must communicate using texting as this places much less burden on the communications systems.