Saturn runs lean - 2002 Saturn L-Series

Bank 1 is generally the cylinder bank closest to the firewall. Bank 2 is the one closest to the radiator.
Sensor 1 is the one in the exhaust manifold.

If the OBD code says it is running lean, you find it is covered in black soot when you remove it. With the new one in, you may get a running lean code as it is burning the soot out. Reset the code, it is a false positive. Happened to me last week.

https://www.google.com/search?q=sensor+1+bank+2+on+a+2008+saturn+vue+3.5l+v6+location

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Check Engine Light On, P0300 Random Misfire Code. A random misfire means your engine is misfiring, but that the problem is not isolated to one or two cylinders. It is jumping around in a random way from one cylinder to another. A random misfire code usually means the air/fuel mixture is running lean. Replace plugs wires and coil packs.Check crank /camshaft position sensors, check MAFS

Hi Duane:
Think I'll "shoot from the hip" on this one.
Just for the fun of it, check the pcv valve and the related vacuum lines.
The auto choke when cold means running rich and the fast idle is OK. When it warms up it wants to run lean and it sounds like it might be too lean. PCV or vacuum leak may be the problem.
It also would be a reasonable idea to to a carb flush and to add a conditioner like SEA FOAM to help clean things up if the fulel gelled while it was parked.
Hope this helps.

Too much gas is rich...not lean. What does it do at idle? Blow black smoke and load up or shake and almost want to stall

Lean running condition A lean running condition means that the air/fuel mixture is unbalanced, and that the engine is getting either too much air, not enough fuel, or a combination of both. Optimally, this ratio should be around 14.7 parts air to 1 part fuel by mass, at low or cruising loads. This ratio is known as stoichiometric for gasoline. Ideally, at WOT, you should aim between 11.5:1 (Rich best torque at WOT) and 13.3:1 (Lean best torque at WOT).
Running lean, like having your spark timing too advanced, creates much more heat during the combustion process. This can lead to piston seizure, a hole in the piston, melted spark plug electrode or other complications due to overheating. You will not be producing peak power, and your exhaust will also emit more oxides of nitrogen, arguably one of the worst byproducts of gasoline combustion for our environment.
Common causes of a lean running condition are an improperly tuned carburetor, clogged fuel line, clogged fuel filter, or a vacuum leak.
Preforming a plug chop is a good way to find out if your engine is running too lean, as you will see a powdery white residue on your spark plug in the presence of a lean condition.
On the other end of the spectrum, richer ratios will also cause lost power, however this will most likely be accompanied by black smoke (around the 9:1 fuel/air ratio area), and fouled spark plugs.

try changing the oxygen sensor

It isn't a restriction. Cat's glow red when the engine is really lean or the timing is wrong.

I had exactly the same problem .Mine was corrected with replacing the O2 sensors .The sensors cost less than $30 each but cost about 20 mins labor per sensor .So if you got an honest mechanic the total cost will be around $130 .

most likely this is the O2 sensor for that cylinder bank is defective.

Yes, it makes sence. I have a 1998 Saturn SL too, and I had to replace the fuel pressure regulater on it. I also had the light go on every once in a while. I asked a guy at saturn, and he said that there was a sencer on the engine that is goes bad after awile. The problem was that it was made of plastic and it would crack, but now they make them out of metal. I don't remember what the sencer is called, but ask a guy at the saturn parts window, and ask him if he knows what the secser is called, he should know.