Thanks all for the help. And thanks for the offer dugg. That would be the part, but.....
I dropped by Lowe's last night and was wandering aimlessly at the water filter aisle just in case. I was about to leave to the plumbing when a sales associate walked by. I asked if he had a second and he was VERY friendly. I took the hose with me and said I need this part to fit a washer outlet. He said, he knows exactly what I need. In about two minutes, the guy has walked to the plumbing section and picked up all the supplies. He takes it over to the PVC cutting machine and says, this is what you do.... He had grabbed brass fittings since it was cheaper than plastic and a plastic compression ring. He takes all the parts, opens the package and said. "Knock out this piece of brass here....." *Whack with a tool and it pops out*, ".....put this brass piece on first, the compression ring, this thing goes in the hose, and it screws together *screws it together*. It was just what I was looking for.... Sort of. He had a different idea of where on the piping it was going. I explained it to him a little better, and in 30 seconds we had all the parts that I needed. $5 and some change later, I'm out the door with a way to fix the RO Unit. I'm impressed with this guy. Extremely nice, fast, and even does the work for you, hands you the packages to be scanned in, and returns to work! Unfortunately, I didn't feel like much effort actually hooking up the RO Unit last night, but I made enough of an effort to have it ready.