They talk about that idea every year, in connection to the ice fishermen needing rescue out on Lake St. Clair. I am very leery of charging a per-call fee for police and fire service.
First off, our taxes already pay for the salaries and equipment. These fees would be "play money" for the government, enabling them to go hog-wild in the gadget catalogs. (Some of which are valuable, like the IR cameras for fire service. If it's that useful, though, then vote on a bond issue to buy some.)
Secondly, it's already possible in Michigan (at least; I don't know about elsewhere) for the prosecutor to force the defendant to pay the prosecutor's time and court costs, etc. That will generally be enough to run any normal defendant into a life of bank robbery or bankruptcy.
Thirdly, it's in society's interest to have police and fire service, so we should not single out any one group upon whom to rest the financial burden.
Fourthly, charging a per-call fee will be a major disincentive to report activity or trouble or need of rescue, for fear of being sent a bill. We should not place a price tag on human life or our public peace.