Cold Start stutter

[SixBanger]

Since last Friday I've had this issue at cold start. After start up it takes me 2 minutes to get out of my driveway in reverse and drive off. When I'm driving in first and second gear I get this stutter when accelerating and I can feel it too. I've had my car at the dealership since Saturday afternoon and the advisor never got back to me until my 3rd phone call to him. He said they don't have any codes nor have they found any hesitation or stuttering while accelerating after cold start. I'm going there first thing in the am and driving with the shop foreman. Am I missing something?
It reminds me of when my first fuel pump when actually, and I was in a parking garage. The car was going in/out and stuttering until it finally died in the garage. Could this be my fuel pump?