I notice that if I accelerate quickly eg "Floor" the gas pedal or come close to flooring, causing the RPM's to go up quickly, once I slow down, the car feels like it wants to turn off, and is very shaky when it idles.

2005 Cadillac CTS 155k 3.6L V6

I know my car is high miles but this has been happening since 50k.

Does anyone know what could be causing this? Has anyone else experienced something similar?