The non-emergency phone lines have great promise as a way to improve services for citizens and to evaluate the job that government is doing (you can find out whether potholes are being filled in five hours or five weeks). However, it's the simpler (though no less important) goal of preserving 911 for emergencies that usually gets localities interested in 311 in the first place.
If you don't think that non-emergency calls to 911 are a major problem for local governments, just look at this excerpt from an article on the gasoline shortage in the South from Tuesday's New York Times :
In Douglas County, Ga., the police issued a request for motorists to stop calling 911 for help finding open gas stations. A county spokeswoman said the calls could interfere with the ability to handle emergencies.