The problem is, in Pittsburgh the two major enterprises/employers are colleges and hospital systems. Both non-profit and both tax exempt. They own a tremendous amount of land (tax-free) employ the most people (tax free) and use up a tremendous amount of city services (such as police, ambulance, fire, water, sewage, etc, all tax free).
The city has been trying for years to get the universities and hospitals to pay something, ANYTHING to help the city with its budget situation. In other cities where non-profits make up a large percentage of the area, the non-profits usually contribute something in terms of "voluntary payments", such as in Boston.
What the mayor is doing, is trying to pressure the universities to come to the negotiating table to help support the city in its time of financial need, using other major cities with major university systems as a model. So far, the universities and hospital systems have refused. (Keep in mind, our major hospital system is UPMC (University of Pittsburgh Medical Center).
Luke cares little for this tax and doesn't want it to pass. He want to use it to cause a big firestorm (which obviously it has) and force concessions. We'll see if it works. PA State Reps are already proposing laws to prevent the City of Pittsburgh from being able to tax students directly.
