Its not happening. Its just Obayashi pulling shit out their ass and trying to call it gold. Lets name a few reasons.
1) Materials. The materials for this simply don't exist yet. We are getting closer every few years to making the advances but we basically need to be able to spin out carbon nanotubes as a single piece kilometers in length....For Cheap! Even ignoring cost, we can't do it yet.
2) Location. A physicist can correct me on this, but Japan is the crappiest place to put a space elevator simply due to location and spin of the earth. A space elevator needs to be built at the equater.
3) Money. Assuming 1 and 2 weren't an issue, this one would be. Building the first space elevator is likely to cost something on the scale of building the Large Hadron Collider. This won't be like building the next biggest tower, it will require deep pockets. No company has this kind of cash to throw around, and in the looming economic crisis thats about to fall upon us, neither does any country.
4) Space junk. As IceCream said, theres a ton of space junk up there just waiting to punch a hole in your new fancy billion dollar cable. You can't move the cable to avoid this stuff either. I suspect someone has already thought up a few solutions for this problem, but it sits low on the list. Space junk is going to be an issue for all travel and no one is really interested in figuring out how to clean LEO up. There are some projects/ideas about deorbiting defunct satellites, but stuff like screwdrivers and bolts are the more dangerous objects in orbit.
5) Environmental fears. We haven't entered the era of nanotechnology paranoia but I'm sure by the time a space elevator becomes a likely possibility, it will be one. The common fear I hear with a carbon nanotube cable is that "What happens if it breaks and spread millions of nanotubes across the planet, will it cause cancer? Will we die?!" I rank this one low on the list but it'll likely be an issue.
Here's what I think is going on. Obayashi has just finished building their fancy new tower in Tokyo. Except they have realized a few things. 1) No one wants to move into the place because fear that it will fall over in the next big 8-9 earthquake. 2) They probably put themselves into a pretty big hole financially trying to build this thing and the problem of realty is starting to sink in. Therefore, they release a PR saying they will be building a space elevator in an attempt to garner more positive media attention and kick shares up a bit.