Sounds like you idle sincere is bad try replacing it and see what happens.
There are many reasons why your car might vibrate while it is idling. It could be running too hard for example.
Its could be the turbo your hearing...
Throw out bearing is bad.
crank position sensor
I know that on my 1998 Silverado, if I but the parking brake on, the fulltime headlites turn off while I'm sitting and idling.
I believe it is in the ball park of 14 to 15 psi of boost. That is what my turbo talon run. Edit: A stock 1g DSM (Talon eclipse laser) has it set at 9-12 PSI. while the stock gauge says 14 sometimes it should not be trusted. get a aftermarket boost gauge and find out yourself
Their pectrol muscles move their wings up and down while running to create lift.
Effectively all the fuel that it burns while idling. You are getting 0 miles per gallon while idling.
It's been a while since I worked on a 1G Talon, but I believe the water Pump is located on the serpentine belt. It's the same belt with the crank shaft and alternator. No, you should not remove the timing belt.
Cooling fan may not be working as it should. If it is not coming on either the fan is defective, fuse is blown, or the thermal sensor is bad. If it is running and the engine is still overheating the radiator may be partially clogged.
There are several things that can cause your Jeep to stall while idling. The timing may be off or your fuel filter may be clogged.
As long as your car engine is running, it should be OK. An exhausted battery will only become a problem when you try to start the car.