Can you drill a hole in the side of your base cabinet and run the water line? You can tap into the cold riser feeding the kitchen faucet.

I forgot to mention it in my orginal posting but the fridge is across the room from the nearest water source.
It is a span of about 6 ft (directly across) from the kitchen sink.
How would I go about snaking it through the wall or ceiling? Without ripping out all the drywall? We know that the joists (in the ceiling) go the opposite way.
Thank you for your first reply...Hope to hear back from you again...

Geeze Tilley, I'm at a loss. It's either the wall, ceiling or floor then. Take your choice of jacking out the concrete or cutting a channel in the drywall. The studs going other way...hmmm....then drill them. ice maker line will go in easy enough, whether your using 1/4" soft copper or plastic tubing. Good Luck, Tom

If the kitchen sink is close to your frige, purchase a saddle valve and put on cold water line of incoming water to kitchen faucet. you can use 1/4 plastic tubing or 1/4 copper either. run through cabinet or along the baseboard. make sure you put above the cutoff on the cold water line in case you ever need to cutoff the water source.

It seems like you would be able to go through the ceiling easy enough. The copper tubing is stiff enough that you would be able to push it down to the hole by your refrigerator. The hole might have to be wide enough to actually get you hand back there, but it's behind your frig anyway. You could do a mediocre patch job and noone would know the difference.

The part I worry about is the line freezing in the attic. You won't be using this much during the winter so you may have to shut this off and drain it during the winter. What do the plumbers think about this???

Good luck,
Devildog