I believe we all have this. Seems it comes with "Throttle by wire". Had the sme hesitation in a corvette when they went to non-linkage. You will get used to it.
And yet we have another thread where the folks are saying that at 50+ MPH, when they it the gas, the car almost stalls and then catches. They have all decided that that is normal too.
I have noticed no hesitation on mine, so do not believe it has anything to do with drive by wire.
After all, that should be done in a few milliseconds. And that should be not detectable by the average driver.
It is intentional, I cannot remember if it is documented in the owner's manual or in the promotional literature but it is designed to make control smoother at low speeds. I had another vehicle with electronic control without the variable algorithm and it was annoying when hitting bumps at low speeds as it made it difficult to keep the power level where you wanted it.
I've experienced a "stall" (just long enough to think that the engine has died before full power kicks in) on several occasions during a DECELERATION (foot off accelerator, sometimes foot on brake) to ACCELERATION (stomp accelerator) sequence - e.g., when approaching a slow moving vehicle and changing lanes to pass or when turning left onto a side street, in the presence of oncoming traffic.
I haven't noticed this behavior on my CTS (DI, RWD, FE2) and I have had to do this sort of maneuver several times recently due to slow moving agricultural traffic. My CTS was produced in early May so I wonder if there have been any software updates since your CTS was produced? I am very familiar with this type of behavior as it definitely got my attention shortly after I bought my '06 pickup and pulled out to pass on a 2 lane highway. At around 52 the pickup shifts into 2'nd overdrive and will stay there down to around 45 and when you suddenly go to full throttle at this point there is a perceptible delay before there is a downshift and fuel flow is increased. I have always assumed that this was probably due to the need to protect the transmission during shifts (the Allison automatic also uses computer controlled clutch to clutch architecture) and perhaps partially due to turbo lag and if you either switch to manual mode and select a lower gear or change to tow/haul mode which is the equivalent of sport mode for the Allison then there is no delay and full engine power is available immediately. In any case, once the rain goes away I will see if I can get my CTS to mimic this behavior and I will post back if it does.
Does selecting sport mode on your CTS make any difference with the delay?
I have been after my dealer to do something about the delay in accelerating, they and Caddy say it is normal and there is no fix in the works. Blows my mind that all those professional reviewers didn't come across this problem. I have had close calls with other cars and trucks, when I have needed to get going, and nothing happened ( live in Boston area ). To me this is a major safety issue that shouldn't be on a 300+ HP car costing close to $50K. I have never had a car do this, from my first '77 AMC Hornet Wagon, to my most recent '05 SRX. Hope there doesn't need to be a bunch of wrecks before Caddy fixes this. Wishing I never bought this car!
Re: DI Throttle Response below 2000 RPM 
