Have I got these simple power calculations right? (for battery consumption)
Your AA battery won't provide the 2V for the LED, so you'll need two of them in series. I guess the 1.2V is the cell voltage, so you have 2.4V for two cells. Your LED would then be dissipating 20mA x 2V = 40mW, but the total load on the battery is 20mA x 2.4V = 48mW. The extra 8mW will be dissipated in the LED's series resistor.

So battery life (2 cells) is 4Wh/48mW = 83 hours, like you calculated.