Fresh rebuilt motor, won't idle

I have a 2001 xj 4.0 that I just recently rebuilt the engine. If I start it after it setting over night it will fire right up, AND it will idle. But once it has ran for approximately 3-4 minutes it will not idle without depressing the gas pedal slightly . I have not yet let it sit at an idle for a long period of time. I broke in the rebuilt motor as needed. And if it dies it won't start unless it has completely cooled down. This is similar to the problem I was having with it before i rebuilt the motor except before it would start hot or cold but still wouldn't idle after warming up. I've replaced almost almost all sensors, tps, crankshaft position sensor, coolant temp sensor, oil sending unit, map sensor, idle air control two times, it has brand new optima red top battery and a brand new alternator. It will pop and sputter when cranking on it and will start maybe sometimes after it has warmed up. The only thing I changed in in the motor was the camshaft, I bought an Elgin RV cam from Titan engines and it runs just fine when I start from a cold start. I'm stumped. I've spent hours researching. Nothing

fuel pressure? Did you check it?

Haven't checked the pressure but alot of it sprays out after it has ran for awhile, I have brand new injectors also.

The timing right? Both dizzy and cam to crank.

Yes

it's obviously a preexisting issue... how clogged is your cat?

I have run into this, especially if the injectors sit for a long time. They get clogged or sticky and just don't work correctly.

Run a can of BG44K.

If you can get your hands on a scanner that will show if the engine is in open or closed loop operation, watch for the switch to closed loop and see if things go to crap before or immediately after or if there is no time connection between the two events (open ---> closed loop & running fine ----> running poorly). This will help narrow it down.
My memory is suspect but I think I have heard of oxygen sensors causing this sort of issue, which would make sense with the computer going closed loop, taking input from the 02s and suddenly not wanting to idle correctly... I'd look at which mode the computer is in when things head south before replacing them, though.

O2 sensors are new, as well as injectors. Yes I am thinking it is a computer issue. I have handed it over to the guy who did my block. It seems to act like something is wrong with fuel or computer. Everything else is brand new

New doesn't not equal working. Just saying.

you can try unplugging each sensor and see if it'll run better. it'll throw a code, but if you can narrow down what sensor makes it run ok, maybe you can find your culprit.