Sounds like the beginnings of death wobble. It could be something as simple as the alignment, or something worn out in the suspension. Steering stabilizers just mask problems.
Have someone turn the steering wheel back and forth and look for any independent movement of the steering components. Especially check the trac bar at the axle. Then jack up the front end and grab the wheel at 12 and 6 and shake it to see if there is movement of the wheel. do the same at 3 and 9. There is a bearing in there and ball joints that hold the knuckle on. if there is movement at 12 and 6 but not at 3 and 9, it's probably the ball joints. If there is movement both ways, it's usually the bearing.
check for leaking fluid from the shocks. If they are leaking they are bad or going bad (steering stabilizer too).
My 99 TJ was doing the same thing, the tire shop had set the alignment toe-out. I had it re-aligned and it fixed the problem.
Good luck.
