This seems like an incredibly difficult and ambitious idea. I'm not sure that the proponents recognize this by orders of magnitude. I don't say that it is impossible, but that it will be very, very, very difficult and expensive. Sometime back, I undertook a small exercise to determine very crudely how much effort would be required. I decided that it could be possible someday, but that it would be a long time off.
First, its length wouldn't be to Earth-synchronous altitude, but roughly twice that far. Reasons and implications of this are:
a) Earth synchronous altitude is necessary for the cable's platform to orbit the planet at the same rate at which the planet turns (to keep the cable roughly straight). As the cable extends down, however, this (one revolution per day) rate is not enough to sustain the cable in orbit, it will go from weightless to progressively heavier as the cable extends down, to the full weight at surface level. This imposes not only an enormous tensile strength requirement on the cable, but also a huge weight on the orbiting platform (or whatever is there) at synchronous altitude. To keep this weight from pulling the 'platform' down, the cable would have to be balanced by a roughly equal cable beyond that platform, so now we have a cable roughly sixty thousand miles tall.
b) The platform is now being pulled in both directions (an equal amount, in order to balance out the forces and keep the platform from being pulled down). This means double the tensile strength requirement. My intuition is that this will probably require something orders of magnitude stronger than 'nanotube' structures. (I leave it to others to determine.)
c) Orbital characteristics will cause the cable to try to wrap itself around the Earth like a maypole, especially as it is being dropped and extended from the platform. This will add additional loads and complications.
d) In order to stabilize the platform(s) in orbit they will possibly have to first be linked with an additional series of cables that circle the Earth (at synchronous altitude. This would add the need for a set of cables roughly two hundred thousand miles long. The saving is that this cable would be weightless, and not add the strain of its weight.
e) As the cable comes into the atmosphere, additional problems will accumulate.
From this I feel that the cost will be a lot higher than proponents estimate, (more likely, closer to ten trillion dollars than to ten billion). It would probably be easier to build a suspension bridge to Hawaii, but that's just my feeling.
KM
