In this paper, we address the problem of powerefficient resource management in Cloud Radio Access Networks (C-RANs). Specifically, we consider the case where Remote Radio Heads (RRHs) perform data transmission, and signal processing is executed in a virtually centralized Base-Band Units (BBUs) pool. Users request to transmit at different time instants; they demand minimum signal-to-noise-plus-interference ratio (SINR) guarantees, and their requests must be accommodated within a given deadline. These constraints pose significant challenges to the management of C-RANs and, as we will show, considerably impact the allocation of processing and radio resources in the network. Accordingly, we analyze the power consumption of the C-RAN system, and we formulate the power consumption minimization problem as a weighted joint scheduling of processing and power allocation problem for C-RANs with minimum SINR and finite horizon constraints. The problem is a Mixed Integer Non-Linear Program (MINLP), and we propose an optimal offline solution based on Dynamic Programming (DP). We show that the optimal solution is of exponential complexity, thus we propose a suboptimal greedy online algorithm of polynomial complexity. We assess the performance of the two proposed solutions through extensive numerical results. Our solution aims to reach an appropriate trade-off between minimizing the power consumption and maximizing the percentage of satisfied users. We show that it results in power consumption that is only marginally higher than the optimum, at significantly lower complexity.