Reading this article spurred me to think on the problem a bit again. The primary problem is that the elevator is too heavy because it is just too long, and it's too long because of the insistence to anchor it on Earth, necessitating geosynchronous orbits. However, what if you just let the bottom of the thing float freely some 45-50k feet above Earth's surface. Sure, you'll need high-altitude planes (which we currently have available) to get to the base-station, but you no longer have the requirement of a geosynchronous orbit. This means you can make the elevator much, much shorter, significantly reducing the tensile stresses and put them well in range of current nanotube materials strength. The caveat, however, is that you still need the anchor in space that maintains the center of mass at a stable orbit. Also, the anchor needs an active propulsion system to keep the elevator in orbit against atmospheric drag. The base-station at the bottom could also have jet engines that assist with keeping the entire elevator in orbit by supplying additional momentum to the elevator.
With a free-floating elevator, you wouldn't need an elevator that's 100,000 km long. You'd probably only need one that's 300-1000 km long. However, it is possible you may need a lot more fuel to maintain the orbit. Although, ion propulsion and electrically powered jet engines could probably be used to mitigate direct fuel usage, and, of course, these propulsion systems would be powered by electric solar panels attached to the anchor in space and, possibly, at various points along the elevator's track.
The other issue with the free-float elevator is that you will need to track its location, and it will likely be moving extremely fast relative to the Earth's surface in order to maintain orbit. It really depends on which orbit the center of mass is placed. The lower the orbit of the center of mass, the faster the entire elevator has to move relative to the Earth's surface to maintain orbit.
I think both these issues can be overcome with some clever engineering such to make the free-floating space elevator a much more feasible idea than either the geosynchronous ribbon from space or the tall tower (which I think the wind is just going to blow that right over without a second thought) that this article reports.