1991 Cadillac Allante hesitation

Probable causes to hesistation and stumbling:

Oxygen sensor/s
Dirty fuel injectors (cleaning the injectors often fixes this).
Bad MAP (manifold absolute pressure) sensor
Bad TPS (throttle position) sensor
Bad or dirty MAF (mass airflow) sensor
Low fuel pressure (leaky fuel pressure regulator or weak fuel pump)
Vacuum leaks (intake manifold, vacuum hoses, throttle body, EGR valve)
Bad gasoline (fuel contaminated with water or too much alcohol)

Sometimes, what feels like a hesitation is actually ignition misfire rather than lean misfire. The causes of ignition misfire may include:

Dirty or worn spark plugs
Bad plug wires
Weak ignition coil
Wet plug wires

Popping back through the intake is a sign it may be running lean. A possibility that the coolant temp sensor is registering warmer than it actually is, and the fuel mixture is not rich enough to satisfy cold running. Another possibility is carbon deposits on the valves that is absorbing some of the available fuel. If you can navigate the onboards, check the coolant temp prior to a cold start and check that it closely resembles the ambient temperature. Try starting cold with your regulator disconnected, line plugged, and see how it does. If it don't act up, then you know it's fueling. Run some top engine cleaner through it, in attempt to rinse some carbon.

Could be the CTS out of calibration test its resistances hot and cold see below chart