The cable ends at the throttle pulley. When you press the gas, the pulley rotates, and in turn extends the kickdown cable, which is the cable extending fron the bottom of the pulley. You'll see two nuts holding the end of the cable housing to a bracket just aft of the pulley. These are the adjustment nuts.

If you pull the kickdown cable by hand, it should spring back with ease, and retract fully. If it doesn't, lubricating it will usually help. I use some spray synthetic lube. To lube the cable, remove the end from the pulley (freeing the cylindrical "anchor"), and remove the housing end from the bracket, so that you can hold the cable up vertically. Carefully and slowly spray some lubricant into the end of the cable. Then, work the cable in and out. Do this about 4 times until you feel the cable move more freely. When putting everything back together, take care to maintain the original adjustment of the two nuts on the bracket.

Another thing: the cable should have a little slack when the throttle is closed. If there is no slack, the cable needs to be adjusted. There are specific methods for adjustment, but I just make tiny adjustments and test drive the car until it feels right. Of course, this assumes that the lubrication doesn't fix the problem.

Sometimes, the cable is too worn out for lubrication to help, but it fixed my problem (which was the same as yours), and it's been fine for over a year now.

Best of luck.