One plan for a road said that it would cost around 2 billion dollars, if done on the cheap. If you are actually including the fact that most major projects like that go over budget you could be looking at 3 billion or so dollars. The terrain is some of the most hostile to road construction in the world, outside of places like Greenland and Nunavut. Add that to the fact that the closest road is the Alaska Highway which is nearly 450 miles east of Juneau and you have a major construction project on your hands.
Well, I don't know about anyone else, but this sounds like a job for Ted Stevens, preferably inserted as an add-on onto a piece of legislation praising kittens for being cute.