The throttle is way too sensitive, the gearing freakin' sucks, and the engine needs an overhaul. You can see how dramatic the change in EPA fuel economy ratings are when you compare the 2004-2008 engine to the 2009+ one. And not too much changed other than the placement of the waterpump onto the accessory belt, and a variable-valve timing mechanism. GM definitely has the potential to create a subcompact killer for fuel economy.
If they can get 37 MPG out of a 2.2 liter in the Cobalt, they can get even better with a heavily revised Aveo.