A Wrangler, especially a SWB Wrangler is limited mainly because of it's short wheelbase. After that, the limiting factor becomes the brakes. The wheelbase is the primary reason that the factory claims 2000 lbs as the towing limit. It has very little to do with the vehicle's ability to move a trailer, as much as the vehicle's ability to control the load it's towing. A short wheelbase doesn't offer much stability for towing, and will let the trailer "push" the vehicle around while cornering, steering around curves, etc.
For brakes, the stock brakes are fine for a stock Jeep, but can be overwhelmed by larger, heavier wheels and tires, not to even mention adding the extra weight of a trailer/load to deal with.