Oh, I assumed your last comment meant that the material would be coming from the moon and/or asteroid belt, and usually people aren't proposing sending humans out there to mine them but von Neumann machines.
Ok, so we send a pair of robots to an asteroid and let nature take its course ...
And then a few generations later we have thousands of robots heading back to earth to build an elevator for us. Yeah, that might work. And it might be cheap. But it probably won't be particularly quick. Maybe 40 - 100 years from first arrival of robots at asteroid, I'd guess. I still don't see how the argument is weakened by the existence of robots, but I agree it is left pretty weak.
http://www.slate.com/id/2283469/pagenum/all/
It's a long article, but the most relevant stuff is at the end, about how we're pretty much locked into the existing rocket technologies: