I have a 96 2.2L Sunfire and it seems to have a problem, but I don't know how serious.

After starting it up and driving for a little while, usually around 3rd- 5th gear (I have a 5spd), the car suddenly seems to lose its power. I can feel the car studdering and shaking like there is a lack of something (fuel?) getting to the engine. There is no pattern to the problem, it can happen after a cold start or while still warm, or when it both wet and dry. So I drop it to like 3rd gear and push the gas and the car simply does not accelerate and just sputters. I know by now that the car is going to stall so I usually pull off the side of the road. If I stop completely with my foot off the gas, it will stall. If I put it in neutral and gun it it will knock the car back into working order and I can drive normally for as long as I want. It only happens once per trip, if ever. Sometimes I can go days without a thing happening!

Another thing is that it usually restarts easily after the stall, but sometimes I need to start while applying some gas. These symptoms seem to point to something wrong with the fuel system (fuel pump maybe) but the car is not breaking down all the time. Is it just on the fritz? Is it something I should bring it to the shop for? I'm not exactly looking to pay for a new fuel pump

Could be many things, but here is some info I posted previously when I had this exact problem on my 96 2.2 that I rescently finally solved.
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There has been much discussion here (including myself) regarding stalling problems with the 2.2. My 1996 Sunfire 2.2 has suffered this problem for several months now - never throwing a check engine light or any codes. It seems many of us were unable to locate the source of the problem. I, like many others, had replaced all the 'suspect' and 'likely' parts without correcting the problem.

For those of you still trying to fix this, and like me have already replaced most or all ignition parts, fuel parts, sensors, vacuum lines, etc, here is what actually fixed mine.

After much wire poking and prodding I was able to locate an intermittent wiring fault. The fuel injectors have 5 wires - 1 wire signal/ground from each injector to the PCM, and 1 common 12V power supply that splits to supply each injector. The 12V power wire was intermittent at the main engine harness split at the most inaccessible location - just below the heater core hoses, at the rear of the block left side (just above and to the left of the ignition coils). Basically the injector 5 wires join a sub harness with the MAP, IAC and TPS wires, then run down to the main harness. It was where this sub harness (about 20 wires) joined into the larger main harness where the intermittent was.

As it was not possible to reach and repair this wire without engine removal, I spliced in a new wire and ran it separately (in a new protective sheath) from just below the injector connector at the left of the intake manifold, to the main harness at the front left of the engine where it was much more accessible. What was happening was that as the engine moved slightly under varying loads, all injectors were losing the 12V power supply and the engine would just quit - at any speed. If it reconnected quick enough - it would catch itself and not stall. Other wise it normally would start right back up again. The connection was generally 'good' in engine off condition - hence the normal restart without problems. Once I found the right stop to poke, I could stall the engine at will, and if I kept tension on the harness, it would not restart.

With the new bypass wire installed - all is now normal again.

It was very time consuming to first locate, open the harness protective sheaths, then to determine how to repair, and locate the correct wire in the main harness. Hopefully anyone who is unable to fix this problem may benefit from this experience.
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Good luck.

Thanks for the info... it sounds like what is going on with mine. Last time I brought it in to be checked the diagnostic found nothing wrong. But I guess if the wire is intermittent, then the diagnostic would not catch it?

I was wondering why the stalling always happens around 3rd-5th gear (around 20-50 mph) or when slowing down from higher speeds (but again the sputtering only happened at low speeds). I guess the shift in the engine could be pinching off a connection... this seems like a difficult fix for a novice... would a auto shop tell me they have to remove the whole damn engine if I told them this? Is there a way to get in there and make an easy fix without them charging me lots of $$?