This could be a bad engine or transmission mount. I had a similar problem with my 2009 Impala LTZ. The problem was collapsed front engine mount which caused the car to shake at idle when stopped. Replacing the mount fixed the problem.
I had a mechanic look at it. He shook the engine and had me press on gas a few times and said that the mount was fine.. Is this the way to check the mount or is there another non invasive way I could check?
There are two engine mounts and one transmission mount on this car. One should take a close look at each mount to inspect for cracks, deterioration and separation of rubber, etc.
