Just replaced CPS, and plugs. Cleaned IAC and throttle body.

Car will die while driving. Has rough time starting
All symptoms worsen after pumping any amount of gas.

Holding gas down usually helps with rough starts.

Car sometimes idles at or below 300RPM

Occasionally when car dies while driving it will start and then die right away again. Holding gas down will spike RPM's up on start, and RPM will studder up and down until it stalls out again.

Starter sometimes seems to crank very slowly, that when it has a rough time starting. Volts are fine however.

No lights, gauges don't do anything unusually.
01 Cherokee Sport

 

What does the fuel pressure look like?

 

could be either a bad fuel filter or your pump is going out, maybe a grounded wire on the pump is causing it to short. i would replace the filter first though and see if that helps.

 

Check your fuel pressure and all your grounds.

 

I see you replaced the CPS....what about the throttle position sensor. Sounds very similar to what my 01 was doing and this was the culprit.