We consider a distributed detection problem where nodes in a wireless sensor network (WSN) report their local decisions to a fusion center that can in turn describe the phenomenon under observation. For such networks, energy- efficient and minimum delay designs are well motivated for a number of applications including surveillance and monitoring in tactical and environmental scenarios. We aim at designing a distributed detection scheme that achieves minimum reporting delay of events and respects constraints on battery life time (or power consumption) and probability of erroneous detection. Our design exploits the interaction between both physical and medium access control (MAC) layers. It attains energy efficiency by using a sleeping protocol whereby monitoring nodes can deterministically switch between awake and sleeping modes to utilize efficiently their power resources. This novel protocol capitalizes on an energy-efficient ternary modulation scheme we devised recently and exploits characteristics of the phenomenon under observation. The resultant cross-layer design is flexible to trade-off latency for energy consumption (and thus life time). Furthermore, it provides the designer with a suite of tuning parameters that can be adjusted to best fit the underlying application. Simulated experiments corroborate our analytical results.