A blinking check engine light in indicative of cylinder misfire, which explains the sputtering.
How many miles on your car? Have you replaces plugs and/or wires yet. I had a similar problems on my 2005 Aveo during cold starts. Turns out I had a defective coil pack, which thankfully, is pretty cheap.
Amazon.com: Standard Motor Products UF-503 Coil: Automotive.
If that is not the problem, I would check/clean your throttle body, TPS, and/or fuel injectors.