An 87 Wrangler has the 4.2L motor in it. And although it should be smooth throughout the entire RPM range. at 3000 you are above the operating range. The 4.2L max is around 2600.
It is designed as a low end RPM torque motor. It isn't designed to be run in the higher RPM range, like the 4.0L is. Although it can climb into the higher rpm's, it is just basically a waste of gas. There is no performance gains from running it that hard.
To get back to your reason for the cough. Although it is possible it could be 1 of the stepper motors on the junky stock carb, it is most likely valve train lash, or for a better word, slop in the timing chain. Unless the chain and gears are fairly new, the tensioner gets wore and allows the chain to slop back and forth. The chain runs from a gear on the crankshaft to a gear on the front of the cam shaft. The cam moves push rods that open and close the valves. Your cough comes from the cam not catching up with the rest of the motor due to too high of rpm's.
Stay under 2600, and the motor will perform fine.
