jackrae:
If they're something like CR2032 then they are rated at less than 1mA, which is a lot less than your micro is demanding. Coin cells are really not suitable as a power source for anything other than memory retention or running RTCs.
CR2032 can power a very small 5x6 scrolling message for 2 days but that's it.
It has peak current of a few mA since the LEDs are so small they have their own resistance.