It is possible to just tap into the 110-volt AC. Also if they are transmitting at very low power and short range, a good lithium battery can last 10 years.
I've gone to some electronic parts seminars where the vendors talk about "permanent" batteries because the life of the battery is longer than the useful life of the device.
Wow, didn't know they could last that long. Just playing devils' advocate. I have little doubt the Clintons are that devious, mind you...