My TJ did that a lot. I changed the plugs...no difference. Then one day the RPMs dropped and it stalled. Turned out to be the throttle position sensor.Since day one, mine likes to drop rpm when at idle. It will drop down to about 300-400 rpm and then kick back up to normal very quickly. It almost stalls out. Dealer has never found a problem.
it's not a "shake". it is so minimal that you have to really sit there and try to feel it. and once again it doesn't feel like it's going to stall either, just the slight shimmy! thanks anyways though...Mine doesn't shake at idle, but every so often when at idle the rpm will drop down to 300 rpm or so and it feels like it is going to stall, but never does.