[Overdriven]

drill press, with the shaft in a vise. Use light pressure or you'll break the bit and use oil to lube and cool. Also set the drill press on a low speed. I did it once on a maxx shaft, took 1/2 hour and 3 bits. Those shafts are hardend steel, very tough to drill through. The dremel can be used to make a small flat spot on the shaft and make it easier to start the hole.

Edit: To reduce the chance of breaking bits, slide them up into the chuck so only a little bit of it is sticking out and raise what you're working on. With less of the bit sticking out of the chuck, there is less to flex and eventually break if you use too much pressure.