Mutual Aid: For "normal" emergencies, governments have arrangements with each other for mutual aid. For example, a very large fire may exceed the capacity of a city's fire department, so nearby cities will send some of their fire fighters to help (examples, Oakland Hills fire, Santa Row in San Jose). These arrangements allow cities to size their police and fire departments to their normal needs, rather than having (expensive) excess capacity to handle large events that occur very infrequently.
The mutual aid approach works for emergencies and small disasters because such events affect only a small part of the region, allowing the unaffected cities to send immediate assistance. However, in a large disaster (such as a major earthquake), the whole region is affected and all cities are overwhelmed at the same time, so none are able to send assistance to the other. Aid has to come from outside the region, and takes time to arrive.
Planning to fail: The American philosophy is that governments are established to serve the common good. Consequently, government is a set of functions, not the people employed to carry out those tasks. However, this perspective is missing from government plans for disasters: virtually all government plans for disasters focus on supporting the operation of the pre-existing personnel.