LAKELAND, Fla.—When his budget for pencils, paper, and other essential supplies was cut by a third this school year, the principal of Combee Elementary School worried children would suffer.

Then, a local church stepped in and "adopted" the school. The First Baptist Church at the Mall stocked a resource room with $5,000 worth of supplies. It now caters spaghetti dinners at evening school events, buys sneakers for poor students, and sends in math and English tutors.

The...