If the vast majority of the difficulty of getting to orbit, at least low-earth orbit, is the horizontal speed and not vertical height, then that suggests a device different from a space elevator. Achieve the horizontal speed on the ground in a long evacuated tube, then add a vertical component of velocity with rockets. You save by not having to carry (nor lift) fuel for horizontal power. Instead, horizontal acceleration could be done by ground-based methods, for example, linear motor.
Air resistance after exiting the tube will be a very big problem. Maybe extend the tube up the side of a very tall mountain.
This has already been thought of: rail gun.
Inspired by http://what-if.xkcd.com/58/
The tremendous horizontal speeds necessary call into question the usefulness of a space elevator, and also make me wonder whether a space fountain would even work.
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