Serial not working when powering with 3V coin cell

Hey folks,

I have an Arduino Uno and an XBEE shield that I'm using for wireless data read-out. When I power the transmitter board with a wall adapter or with a USB from my laptop, the XBEE communication works. I can see the TX and RX LEDs blinking on the XBEE Shield and I receive the data on my receiver module. However, when I switch to power the board with a 3V coin cell battery, the TX and RX LEDs don't blink and I don't get any data on the receiver XBEE. With the coin cell, I know the board is on because the power LED is on, albeit dimmer than with the 5V sources. Thoughts or suggestions?

Will

Bigger capacity battery.
Coin cells are designed to dribble out current and last a long time.
Arduino + Xbee is more current drain than the battery can suppply.
Put a meter on it, think you'll find the 3V is low.