We consider a class of scheduling problems that we refer to as reconfigurable resource scheduling. This class of problems is motivated by emerging applications that involve dynamically allocating a large number of shared resources to a variety of services. We design efficient online algorithms for certain problems in this class. Our goal is to obtain constant competitive online algorithms where the online algorithm is given a constant factor advantage in terms of the number of resources. The main problem considered in this paper is as follows. The input is a sequence of requests, each of which is a set of unit jobs. Each job has a category, and needs to be processed within a fixed delay bound from its arrival, or else it is dropped and we incur a category-specific drop cost. A job of a given category can only be executed on a resource configured for that category. A resource can be reconfigured at any time at a fixed reconfiguration cost. Our main result is a constant competitive online algorithm for this problem, which is obtained by the following layered approach. First, we reduce our main problem to the special case in which all jobs arrive at integral multiples of the delay bound. Second, we reduce the latter problem to the special case of unit delay. Third, we reduce the unit-delay problem to a caching problem that we refer to as file caching with remote reads. Our solution to this caching problem generalizes certain existing work in the area of file caching.