HuwG, Robinson certainly included a nice disaster scenario in his book. Like most epic disaster fiction though, it makes good fiction but bad fact. Unless there's a force pushing it sideways, what gets dropped falls straight down. You wouldn't want to be within a few miles of the base, but that's all.
As I remember, the idea isn't that we anchor the Earth end, but that we give it the freedom to move around a bit in response to whatever atmospheric wiggles go on. The fixed point has to be the satellite end (where there's a stonking big bit of rock or something as a counterweight), not the Earth end. So putting the Earth end out at sea solves the problem by letting it float around as needed.
NASA has at least two separate projects going for this. One is working on the problem of how to make the cable, and the other is figuring out how to make something climb the cable.