Hello and thank you for your post. I am a master certified GM tech, with 15 years Saturn experience,and can help you to resolve your issue.
is the engine misfiring? (shaking or stuttering on accel?)
can you duplicate the hesitation when in drive and hitting the gas and brake at the same time?(power braking)
does the service engine soon light ever come on and have you had this scanned for codes?
No,the engine is not misfiring. The service engine light came on once a long time ago but has not been on for a long time.
Sorry for the delay to respond but I had to leave for a while.
OK the problem with diagnosing a hesitation without a code to start with is that we need to do a lot of testing to try to figure out why it runs so bad. I can't just point and say you need a blank or a blank.
so, what I would start by doing is checking the orientation of the spark plug wires on the coils.
the cylinders are numbered 1-2-3-4 from left to right (when facing the engine) and on the coils they must be 4-1-2-3.
if 4 & 1 are reversed, bad things will happen.
second, unplug the coolant temp sensor and see if it has wetness or corrosion in the connector. That would indicate a cracked sensor.
then if that is OK, take a fuel sample. Dirty fuel or fuel with water in it will cause this as well.
then if all that is ok, take a fuel pressure reading. It should be at a minimum 36PSI on this engine when at idle.
if all that seems ok, you need to take a compression reading, compare the numbers and they should all be above 125 psi
Take a fuel volume test, you could have sufficient fuel pressure but insufficient fuel flow.
You may want to just replace the fuel filter as a matter of course
If all these basic tests do not lead to a cause, a scan tool will be needed to look at things like fuel trim, map sensor voltage, coolant and intake air temp etc... to try to determine the cause.
unfortunately, a hesitation can be caused by a slew of things so I can't just diagnose it without all this info.
I hope this helps.