We were driving and all of a sudden the engine started sputtering. What could cause the sputter?

There are several potential issues that could be causing your 2005 Chevy Monte Carlo to spit and sputter while driving. Here are a few possibilities:

1. Fuel delivery issues: If your engine is not receiving the correct amount of fuel or air, it can cause hesitation or rough idling. This could be due to a clogged fuel filter, a malfunctioning fuel pump, or a problem with the air intake system.
2. Ignition system issues: A faulty spark plug, ignition coil, or other component of the ignition system can cause misfires, which can make the engine hesitate or sputter.
3. Emissions system issues: Your vehicle's emissions system is designed to reduce harmful pollutants in the exhaust. A malfunctioning component of this system, such as the oxygen sensor, can cause the engine to run poorly.
4. Electrical issues: A damaged or worn electrical component, such as a sensor or relay, can cause the engine to run rough or stall.
5. Transmission issues: If your vehicle is experiencing transmission problems, such as slipping or shifting issues, it can cause the engine to hesitate or sputter.

To determine the exact cause of the problem, it's best to have your vehicle diagnosed by a certified mechanic. They can perform a diagnostic scan to check for any error codes or issues with the engine, transmission, or emissions system.

Spark plugs also cause an engine to sputter when oil has come into contact with the spark plug well. One diagnoses this by testing the spark plugs and visually inspecting the well. If the car is fuel injected, a blocked or malfunctioning fuel injector might be causing the problem.

What causes a car or engine to sputter? ' Reference.com

https://www.reference.com/vehicles/causes-car-engine-sputter-454cdb87ff821c31 ENGINE SPUTTERING Google Search

sputtering is called misfire..
means horrid combustion.

#1 all time cause, world wide, all gas engines, for 100 years
is never getting a tune up.
nothing beats this cause, due to driver driving car till it quits
or sputters.

if low on cash? try new spark plugs...
gapping them to spec, not guessing....

code p0320 refers to cam shaft position (CKP) sensor/engine speed (RPM) sensor--circuit malfunction=== causes --wiring--CKP/RPM sensor ---ECM
because the engine runs ok until it is on cruise control I would be investigating the RPM sensor for a fault
The cruise control takes its control from the RPM sensor and if that circuit is interminable the the cruise control doesn't know what rpms to maintain.

Stop using the car

You have serious cylinder misfires,so severe
you maybe ruining the exhaust converter,thus the smell

I won't write a book on all the causes or fixes,have a
repair shop diagnose

catalitic converter is clogged up its not lettig the car breath

Sounds like your culprit is the fuel pump my friend

check for 12v constant at your fuel pump if you are not getting that replace your relay.
if you are getting 12 volts at your fuel pump the fuel pump is possible to run tuel it gets warm then shut down to a lower rpm I would then replace the fuel pump

Check the fuel filter to see if it is plugged.
Remove the fuel filter, and blow air through it in the normal direction of fuel flow. You should be able to blow through it very easily. If it feels restricted, try blowing through it the opposite way, and if there is a lot of dirt coming out, you have found a common cause of this problem. Hope this helps.