How to drill larger holes in cabinets for larger ice maker tubing but leave something to snake with?
As I was typing my question I had a thought so I'm answering my own question.

My plan is to make a hole at the end of the tubing and tie some cable pulling line (polypropylene string) and snake that through the original holes by pulling out the old tubing.

Next I'll tape or hold down the string so it's away from the hole and drill a hole next to the original hole that's the right size, slightly overlapping the old hole. That will allow me to pass the string from the small hole to the larger one but keep the string far enough away from the drill to keep it from snagging on the bit. 



Then I can tie the end of the stainless braided tubing to the line and pull it through.