If we could manufacture a few meters of space elevator material, that'd be one thing, and I might accept an argument that 'with a Manhattan project equivalent, we could build a space elevator in a decade or two'.
I think you are looking at the wrong problem. Assume that you can easily turn coal into bucktube material suitable for building an elevator. Now, compute how many tons of the stuff you will need. And then, how many tons of chemical rocket fuel will be required to lift all that material up to GEO.
Oh, we may build an elevator some day. But I doubt that the material for building it will come from the Earth's surface.
Assuming von Neumann machines doesn't do much to strengthen the argument 'we could build a space elevator relatively soon if we really wanted to'. If anything, it weakens it...
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: