It depends on the exchange in regards to the power that is being supplied. Larger ones have generators, smaller ones only have battery backup.
The generators are tested monthly and from memory have 7-21 days of Diesel to keep them going depending on their business importance and size of the tanks so that's plenty of time before they will need to be refilled.
The battery only exchanges I think were good for 4 days. They also can take a generator being cabled in if power is going to be off for any longer so if needs be one will be dropped outside.
All DSL cabinets have battery backup to keep them that I think is good for 24-36 hours.
All of the above could be completely wrong as I am going from very vague memory on this.
The comms I have seen today include: 31 PSTN cabinets and exchanges with mains fail alarms running on backup power with varying capacity.
I'm sure the impacts will be minor as this isn't Spark and/or Chorus's first rodeo and Christchurch Earthquake has proven out the BCP plans.
The main impact will be downed overhead cables and how quickly they will be repaired on a per customer / smaller area basis.