RPM Drop When Shifting into D or R When Cold

My '93 XJ (4.0L, Auto) has recently developed an issue where the car feels like it's going to stall when I first start the car and shift into Drive or Reverse. Giving it a bit of gas solves the problem, but I can't back out of my driveway by just riding the brake, for instance. After the engine warms up, everything's fine - no problems, even when restarting the car after letting it sit for a few minutes. It feels to me like a transmission issue - it's just like not properly shifting into first when starting from a stop in a manual car. Does anyone have any ideas on this one? I did a search but didn't come up with anything quite like this.

Please let me know if you need additional information. I'm not a mechanic (I'm an electrical engineer), so I'm not sure where to start looking.

Thanks in advance.