I love that thing. Flying battleships, whether it be Sea Dragon or Orion, are just the tops.
Meeting the price goal should be easy, since paper rockets are always cheap.
The real problem is finding a reason why the US would want so much launch capacity. Satellites are much more sensible than a manned observation platform. ICBMs are cheaper and more defensible than nukes in orbit and cheaper and way more workable than nukes on the moon. If its a vanity prestige project you want, Apollo and the moon is fine, you don't need Gigantor the rocket.
If the Soviets somehow beat us to the moon, then maybe as a vanity project we decide either to go to Mars or to create a Space City or a moonbase. If so, then the launch capacity of a Sea Rocket might make sense.
If you accelerate the discovery and dissemination of the knowledge of dinosaur-killing comets, and then actually discover a comet or asteroid that everyone is convinced will hit earth, then you could get Sea Dragons built that way. But you need the comet/asteroid to be years and years away from hitting, so there's time to build the rockets, and even today we can't really predict cometary and asteroidal orbits verey accurately that far in advance (correct me if I'm wrong).
If the military decides to go hard for the Thor/rods from God idea then Sea Dragon might be necessary to support that, but I just don't see that happening. Bombs are cheaper.
If we discover some kind of evidence of extraterrestrial life, then that might be enough to get us to move massively into space exploration, and therefore to build the Sea Dragon. If we discover an artefact of some kind drifting through the system, that would do it for sure. But some kind of SETI success might be enough, just because it would make space seem more important.
Not really related, but the idea of a Sea Dragon ICBM with like five hundred warheads is really, really cool. Not sure why anyone would do that. It would be called the Sea Hydra, obviously.