Caddy just started surging at road speed with throttle steady. Idles fine, and when you mash the gas performs fine, just surges and jerky at steady throttle about 40 to 55 mph.

This is probable the throttle position sensor. They are about 40 dollars

Is the car equipped with the Automatic Transmission?
If so, read on.
Otherwise skip to the end and answer some questions.

POSSIBLE SCENARIO:
I have observed a condition where my car surges slightly when the torque-converter clutch (TCC) cycles between lock and unlock when driving on an uphill grade.
First some basics and history that will explain why the TCC is used.

Engine, Torque Converter, TCC, and Transmission relationship--
The TCC allows for a solid connection between the engine and transmission which allows the input to the transmission to rotate at the same speed as the engine.
Without a TCC, there is slippage between the engine and automatic transmission. The slippage is greatest at low engine RPM. That is what allows the engine to run with the automatic transmission in gear, like when you first shift into gear or stop at a stop sign. When the throttle pedal is depressed, the engine RPM begins to increase and the torque converter begins to slip less and less the more the engine RPM increases. The car moves. But even at cruising speeds the torque converter slips slightly. Engine RPM is greater than transmission input RPM, which is realized as slight decrease in fuel efficiency.
When acceleration is complete and a constant speed is being maintained, the engine power output is reduced to the point where the TCC can engage and eliminate any slippage between the engine and transmission. If the car has a tachometer the engagement of the TCC can be verified when a slight reduction in engine RPM observed without a corresponding change in vehicle speed.
One method used to test the operation of the TCC is as follows:
Find a flat section of road where it is safe to perform the test.
Reach a steady speed and keep the gas pedal depressed with one foot. While observing the tachometer (or listening for an increase in engine RPM), with the other foot depress the brake pedal enough to activate the break light switch but not enough to engage the brakes. When the brake light switch activates, the TCC receives a signal to disengage. With the gas pedal being held steady, release the brake pedal and the engine RPM should decrease when the TCC engages.
Old cars with Automatic Transmissions did not use a TCC. I believe the TCC was put in use in an attempt to increase fuel economy.

MY EXPERIENCE WITH SIMILAR SYMPTOMS
The condition that causes that issue on my car is this:
- A slight uphill grade increases the load on the engine.
The car tends to gradually slow and it is necessary to depress the gas pedal to maintain speed.
- Depressing the throttle pedal (manually, or automatically with cruise control engaged) signals the torque converter clutch to unlock when the load increases slightly. (A more drastic load increase would signal the Transmission to downshift to a lower gear.) The corresponding increase in engine RPM and output is enough to compensate for the reduction in speed. When the vehicle speed, engine RPM, and throttle position stabilize to the point that the TCC will engage and the engine RPM will reduce in correspondence with TCC engagement. Now, if the road conditions have not changed, power output is not enough to maintain vehicle speed. With the increased load caused by full engagement between engine and transmission, and the cycle (surging) repeats itself until the road conditions change.

Does that help?
If not:

QUESTIONS
Please define the symptoms.
What are the road conditions when the surge occurs? (A slight uphill grade?)
What is the frequency of the surge?
Does the engine power output have a noticeable surge?
Is there a speed change related to the surge?
Does the tachometer move up and down with little or no change in vehicle speed?
Are all instrument indication in the normal range?
What else has changed?

Good luck!

Check your air filter

get the service and repair manual from the given link and fix the problem by you own http://toolsnyou.com/

sounds like its breaking down, check your ignition system, test your leads, check your plugs, check your ignition coils etc etc etc.

ENGINE SURGING COULD BE WEAK FUEL PUMP, STOPPED UP FUEL FILTER,BAD TORQUE CONVERTER SOLENOID OR TORQUE CONVERTER. OR FAULTY TPS.

Check the fuel pump pressure.
Also can replace the fuel filter, cheap and might help.

might be ur throttle position sensor

Did you have the wires replaced also?? If not I would replace both the plugs & the wires all at the same time.You may have carbon tracking on your wires & plugs.What Year is Saturn?? If it's a 91-94 You most likely have a EGR Valve floating due to a weak internal spring.It will cause a surge miss at constant throttle.Hope This Helps!!

Its could be a few things. Most likely cause is you IAC (Idle air control valve) If this valve gets clogged up with carbon it will cause a idle surge on cold starts like you are describing.

Next your FITV (fast idle thermal valve). When the hot wax inside of this valve starts to wear it will cause a idle surge on cold starts.