Blue - I think using the word 'tube' sounds like it's so LARGE. The width of the line going through your vein is TINY!! Honestly, it's not really a big deal and the build up is in your head (which I've dealt with too!). I also actually think it's pretty cool, because you can see it on the ultrasound machine - I'm a sucker for cool medical stuff, so after 2 minutes my mind is totally off of what the technician is doing.
I used to get the same build up of terror the first few times, but after the 15 min procedure, I'm always like "that was easy, why was I being so emotional"? I think it's more about facing the fact that you are sick, rather than the PICC itself =). The PICC is so nice because you can do your IV's from home with NO problems!!!!
Try some relaxation techniques and go for it. I don't think you'll be sorry that you did. It really isn't as big of a deal as we always think it will be! Hugs.