Well, that's kind of the point--to get nations overinvested to the point that they can't easily back out. But yes, with current tensions betweeen the US and Russia they aren't likely to begin cooperation on any new projects for the time being.
As far as seeding our species in space, there's no need for nuclear pulse drives to take us to other systems--our first step must be to colonize our own system, starting with Mars colonies and/or permanent orbital habitats, working towards in-situ resource utilization (i.e., manufacturing new spaceships and habitats directly from asteroids). It isn't a true seed until that seed is able to produce another seed.
The intermediate step towards that end is simply developing more cost-efficient surface-to-orbit launch technologies. Space X is doing good work on this, and Britain's Skylon spaceplane project is also extremely promising. A space elevator, unfortunately, will likely be out of reach of our engineering capabilities for quite a while. While cooperation is beneficial in some aspects, competition is often essential as well, to foster innovation.