I've used a MEGA to program Attiny2313 with no problems. Just don't forget the capacitor between reset and ground (on the mega). Try this line and post the output here (in case it doesn't work).
avrdude -c stk500v1 -P /dev/ttyACM0 -p t2313 -b 19200 -v -v
Edit: This is how everything should be connected (The LED is optional).
Edit 2: The capacitor is 10uF.