Vibration at idle brings to mind a few suspects:
transmission mount(s) broken/missing
transmission internally worn
motor mount(s) broken/missing
(1) transmission internally worn or transmission mount broken/missing - test this by shifting into neutral at the next stop light. If the vibration disappears when you disengage the transmission, then the transmission is the source of the vibration. You'll have to inspect the transmission mounts - if they're ok, then the transmission is internally worn and can no longer smoothly "slip" while idling in drive.
(2) motor mount broken/missing - also test this by shifting into neutral at the next stop light. If the vibration persists, then the transmission is exonerated, and the vibration is coming from (under) the engine. The rubber part of motor mounts commonly crack/break and or pop out and are lost.
A photo of the front motor mount for the 2003 Dodge Neon: