That sounds like a reason for us to be the first.
Glen Reynolds misses a key point. The Space Elevator will need to be built in international waters, and as a result its not going to be controlled by a particular country. You could go out and build it without asking permission from anyone else, but it would be illegal and not worth the cost in terms of political capital. A government effort to construct such a system is most likely to be a multi-national partnership after the lawyers are finished with it, and likely a beaurocratic one at that. It may, however, be controlled by a single entity if that entity is a private enterprise, which is what the article meant when it discussed first mover advantage. The other difference between this project and NASA's proposal is that this project has basic unsolved engineering problems related to the manufacture of carbon nanotubes and high longevity mechanical vehicles whereas NASA's proposal is a straight forward application of technology that has already been invented. In that sense NASA's approach is far more, ehm, down to earth. The government ought to pursue the low risk approach and let private enterprise pursue the higher risk approach, with some support in the form of federal research grants for the basic technology required. Having said all that, I would like to see space elevator technology backed by an Administration level initiative that directs grant funding to appropriate projects. TCS: Tech Central Station - Is This the Right Way to Return to the Moon? | 
