There is often a significant amount of data flowing around in the public sector. When there is a constant baseline of a task to be done for the foreseeable future, it is often less expensive to fill that with a FTE rather than a contractor or consultant.

Things from the city jail management (transferring to state or federal when appropriate - or to the hospital and back - or to the court and back, etc...), payroll (and staffing management), data mining, managing assments of property, scheduling housing or business inspectors, budget forecasting based on weather models, keeping track of all the permits and where they are in the process...

There is lots of places where information technology has a role. Not necessarily high tech, but rather managing the information that is flowing through the system to make sure that the proper data goes to the proper places.

Its not going to be glamorous, but it sure beats paper and excel spreadsheets in email.

While big consulting shops may be brought in from time to time to do a project - the role of integration that software with the existing systems often falls to a FTE employed by the city, state, or whatever. Keeping that institutional knowledge about how things work is often priceless (well, you can put a price on it - how long does it take to figure out the system that Stan left behind... and if that's a consultant doing that, how much are they billing you for that discovery work?). In many public sector shops, the preserved institutional knowledge that a team may have can easily run into the collective century or more. That is a lot of understanding of how things work that can't be effectively outsourced.