I found that the source of the leak was not the supply line but rather a pinhole in the body of the water valve assembly that would shoot out when the refrigerator went to make ice. I ordered the part and had it in 2 days. The following day after getting home from work, I gathered my tools, pulled the fridge out from the wall, and had it replaced within the hour.
One note for other do-it-yourselfers, the water line coming out of the top of the assembly requires a fairly firm pull. After removing the retaining clip, slide the plastic piece up the line. The water line going into the assembly is held in by not only an o ring, but some metal barbs as well. Move the tubing side to side as you pull on it and it will work it's way out. There will be some superficial scoring on the tube from the barbs, but you'll be able to reuse it.
$105 for the part, tax and shipping. Probably saved myself at least $150 doing it myself.