In this paper, we present a framework for the design of minimal power schedulers that satisfy average packet delay bounds for multiple users in a Gaussian wireless broadcast channel. We completely characterize the achievable region in the multidimensional delay-power space, and present schedulers that achieve the boundary regions. The optimal schedulers minimize the transmission power by jointly allocating rate and power to the different users based on various buffer and channel conditions. Finally, we also present low complexity scheduler designs that have near optimal performance.