No resolve here? Ive been dealing with a similar thing just about every time, after sitting the night, on first start of the day. My TJ is garaged, so its not weather related, unless humidity is a culprit. Did it again later this evening, after sitting for about 2.5 hours. It doesnt die on me, it just idles like its misfiring.
Im wondering if its my cam sensor (if that's what its called) as Ive changed my plugs approx 40k miles ago (5 years now) and cleaned my throttlebody, IAC and housing last year. All 02 sensors are relatively new too, NGK brand.
OP, did you figure it out? Cant be my fuel pump, because thats new as of last Aug, and it fires right up, no delay. It's just a weak, misfire for the first 3 to 4 min. I'll post a video in the AM, Thur, for reference.