Power consumption is one of the most significant technical barriers for practical millimeter wave (mmWave) communication devices for mobile applications. Communication in the higher mmWave bands above 100 GHz will face even greater challenges. This paper attempts to provide initial power estimates for mobile mmWave devices under realistic parameter values and state-of-the-art device performance characteristics to understand the performance of such systems today and guide research for the future. Power is estimated for a user equipment in a multicarrier New Radio (NR) system for both a 4×100 MHz system at 28 GHz similar to current 5G deployments as well as a hypothetical 8×200 MHz system at 140 GHz that may be used in future 6G systems. Importantly, the analysis considers power consumption of both the RF front-end components as well as portions of the digital baseband processing. Both analog and fully-digital beamforming are also evaluated.