We consider a mathematical model for streaming media packets (as the motivating key example) from a transmitter buffer to a receiver over a wireless link while controlling the transmitter power (hence, the packet/job processing rate). When each packet comes to the head-of-line (HOL) in the buffer, it is given a deadline $D$ which is the maximum number of times the transmitter can attempt retransmission in order to successfully transmit the packet. If this number of transmission attempts is exhausted, the packet is ejected from the buffer and the next packet comes to the HOL. Costs are incurred in each time slot for holding packets in the buffer, expending transmitter power, and ejecting packets which exceed their deadlines. We investigate how transmission power should be chosen so as to minimize the total cost of transmitting the items in the buffer. We formulate the optimal power control problem in a dynamic programming framework and then hone in on the special case of fixed interference. For this special case, we are able to provide a precise analytic characterization of how the power control should vary with the backlog and how the power control should react to approaching deadlines. In particular, we show monotonicity results for how the transmitter should adapt power levels to the backlog and approaching deadlines. We leverage these analytic results from the special case to build a power control scheme for the general case. Monte Carlo simulations are used to evaluate the performance of the resulting power control scheme as compared to the optimal scheme. The resulting power control scheme is sub-optimal but it provides a low-complexity approximation of the optimal power control. Simulations show that our proposed schemes outperform benchmark algorithms. We also discuss applications of the model to other practical operational scenarios.