I use a wireless infrared optical mouse, and it can last a month (months?) on two AAs. And that is with the IR coming from the mouse, not an external source. The camera on the mouse might be quite a bit lower resolution, though.
It is the combination of several features that worries me. The Wiimote feeding power to the nunchuck (or classic controller), rumble, sound, IR camera, at least two accelerometers, 2-way bluetooth comunication.