Your mass prevents it from happening. As you get closer and closer to c, your mass increases, requiring more energy to accelerate you further.
To actually move at c, you'd require infinite energy. You don't have infinite energy, hence you can't hit c.
Now, the trick with the tube would be this:
Take, say, a six foot by six foot square of material. Lets say light can move 3 feet/second, and you can move 1 foot/second, and you want to get a dinky car, represnting you, from the middle of the left edge to the middle of the right edge.
Light will do that in two seconds. The dinky car will do it in six seconds.
Now, pick up the cloth, and hang it over a clothes line. Hook a dinky-car sized flexible tube from point A to point B on the two edges. They'll be an inch or two apart. Light still travels along the surface, and takes two seconds to get there. Your dinky car, however, gets there virtually instantly.
Your car didn't move any faster, you just warped space to decrease the distance you had to travel.