Federal law allows local governments to deny construction permits for cell towers, however, such denial must be based on a reasoned approach; otherwise the FCC is authorized to preempt the local decision and grant the permit. The 1996 Telecommunications Act preserves local government zoning authority as it relates to cell tower siting, but it provides three key protections for firms seeking to erect a tower:

Local ordinances may not “unreasonably” discriminate among providers of functionally equivalent services. Tower siting policies must not favor one company, or one technology, over another;

Local government may not impose a blanket prohibition against the placement of telecommunications towers; and

Local ordinances may not impose more stringent “environmental effects” limits on radio frequency emissions than those adopted by the Federal Communications Commission (FCC).

Stolen from... I just closed the tab. Anyhow, in some cases the carriers will just throw up their hands and say "fuck, we'll put it somewhere else, enjoy your shitty service" if the locals are piss babies.