Data centers (DaCes) can help decarbonize the power grid by helping absorb renewable power (e.g., wind and solar) due to their ability to shift power loads across space and time. However, to harness such load-shifting flexibility, it is necessary to understand how grid signals (carbon signals and price/load allocations) affect DaCe operations. An obstacle that arises here is the lack of computationally-tractable DaCe scheduling models that can capture objectives, constraints, and information flows that arise at the interface of DaCes and the grid. To address this gap, we present a receding-horizon scheduling model (a mixed-integer programming model) that captures the resource management layer between the DaCe scheduler and the grid while accounting for logical constraints, different types of objectives, and forecasts of incoming job profiles and of available computing capacity. We use our model to conduct extensive case studies based on public data from Microsoft Azure and MISO. Our studies show that DaCes can provide significant temporal load-shifting flexibility in response to carbon emission signals and peak demand charges from electricity markets without sacrificing much scheduling performance. Models and case studies are shared as easy-to-use Julia code.