Engine idle speed inconsistent, then when I step on accelerator engine sputters and dies. If going down the road I push too hard on accelerator engine sputters until I let up a little on accelerator. Its a 1990 cherokee 4.0. Any help?

 

Last time mine did that it was an O2 sensor and my cat convertor. There are potentially 100s of things that could cause this though.
How's your exhaust? How's your maintenance? Refreshed some grounds lately? Done any seafoam treatments? Plugs wire etc?

 

Eventually... if you drive a jeep long enough, and don't do any preventive maintenance, it will start running poorly and quit.

Checked your Trans fluid lately?

 

A spit and sputter on acceleration could be bad gas, TPS, injectors, fuel pump, bad cat, etc.. Lots of stuff, really. When was its last tuneup?

 

Heck, how's your air filter?... could be anything.

 

Ever cleaned the throttle body?

 

Agree with others. Get back to basics.

1. Tuneup. Fresh Champion plugs gapped to .035, quality plug wires, distributor cap, rotor, fuel filter.

2. Test fuel pressure. Should be 31 psi at idle. Now disconnect the vacuum line leading to the fuel pressure regulator and the pressure should jump to approximately 39 psi. Look for degrading of that vacuum line. Raw fuel in that vacuum line indicates a ruptured fuel pressure regulator.

Start there. As noted, there are a LOT of things that can cause this. But this is where I would start if it was in my garage.