The idle power consumption is mainly due to ESP8266. On paper, the current draw of the chip is listed here:
http://bbs.espressif.com/viewtopic.php?t=133
when idle, it’s in Rx (receiving mode), and the current is around 50 to 60mA. I did some quick measurement, and found that the total current draw is about 60 to 70 mA. So if you have a 2000mAh battery, it should last for about 28 hours before it needs to be recharged. The power draw is 5V * 0.7 = 0.35 watt.