It’s true that most local governments have some fat that can be cut from less visible programs and services. However, when the goal is to get constituents riled up and preserve popular programs at all costs (including possible tax increases), it’s much easier to target highly valued services: fire and emergency, trash and recycling, education, parks, and police.
At levels below the Federal government (which has control of the official counterfeiting system (printing presses), local governments, when unable to raise taxes, routinely cut back on emergency services such as fire fighting and police. Additionally, as is the case in the suburban area where this humble blogster resides, police are assigned to "revenue enhancement " duties such as speed traps and code enforcement, often to the neglect of public safety. We have witnessed officers assigned to speed trap and seat belt enforcement neglect to enforce serious safety violations of careless and inattentive motorists.
Recent high profile events have tended to drive home the fact that "when seconds matter, the police are only minutes away"; or as in the case of many urban environments perhaps hours.
Ultimately, the citizen must rely on himself for his and his family's safety/defense against predatory criminals even though police personnel are experts at arriving on the scene and making chalk outlines of victims bodies and festooning yellow tape around crime scenes.