Tim,
I couldn't get your model number to pull up, could you double check it for me? Yes, it sounds like you have a frozen water line. You usually have leave the door open, and let it warm up until the tube thaws out. Make sure the freezer is set in the middle to 0 degrees, if it is set too cold it can cause the line to freeze. Also, when you let the door warm up, if there is any moisture frozen in the door insulation, that should allow it to melt too. GE makes a water tube heater kit, but I am not sure if it applies to your model. You might have to contact GE to see if they can tell you if the water tube heater kit is compatible or needed for your model. I believe certain models within a certain serial number range were affected.
Water Dispenser Tube Heater Kit - Part # PD00001237 (mfg # WR49X10173