Power saving and query processing are two major concerns in a wireless sensor network. Each of these two issues has been intensively studied separately in the literature. In this work, we are interested in linking the asynchronous power-saving protocol and the continuous query-processing problem together. A cross-layer solution is proposed. On the MAC layer, we propose to use the grid-quorum system (Tseng et al., Computer Networks, 43(3):317---337, 2003) to serve as the underlying power-saving framework. On the network layer, we propose to find query paths based on the power cost incurred by grid quorums used by nodes along a path. We show how these two layers interwork with each other to support continuous queries in an energy-efficient way.