I dont know the steps to removing the shifter cable, but that seems to be what you need to do.
But before that - uncover the top of the tranny so you can drip some oil or penetrating oil onto the shifter assembly where it runs into the top of the tranny. That location is close to being 'outside', and doesnt really get lubrication - other than what might splash up onto the shaft inisde the tranny. Uncovering the top of the tranny will likely mean removing the battery and the battery tray. This is not a hard job, and gets easier after you have done it a few times.
Un-do the connection of the cable to the shifter assembly that is on the top of the tranny - and see if its still the cable that is stiff, or if it is the shifter assembly (lever or whatever you want to call it) on the tranny. If that is the problem, you could use any penetrating oil to get it to free up, then periodically bath the region with something like "Marvel Mystery Oil". Its a nice product that acts like a penetrating oil, displaces water based moisture, and is a thin lubricant too. 3-in-1 oil will also work. I try to do this at least once a year, along with oiling the door hinges, and putting a drop of oil onto the ignition key, then putting it into the lock for ten minutes. Actually each lock on the car.
I think its also possible for the pivot at the bottom of the shifter lever (inside the car on the lower console) to get rusty. You would have to remove the console covers to get to this point - and could try penetrating oil on that pivot as well.
If you dont fix the stiffness, I predict you will eventually need to replace the plastic grommets that support the shifter cable (inside the car & time consuming to access).
A Haynes or Chilton manual would have some explanatory steps, and the Chrysler manual for the car would of course have detailed steps and sketches. I got mine on ebay for about $30. It paid for itself the day the UPS man delivered it to the house.