Well, two issues with that:
- If we believe the Project is all about rebuilding ... why aren't we burying our own rebuildy-ness stuff? Though yes, if they only have a very short warning (not enough time to dig more bunkers) the government response might be just a few Special Forces guys. But canonically they have five years ...
- Why use (only) the Project wake-up signal? The government should be able to detect the apocalypse. If only there were some big computer, in a super-secret bunker, with super-hardened communication links, hidden deep in the wilds of Michigan!
As an aspect of strategic planning, you'd think Damocles would be told about the Morrow Project and the Snake Eaters. "Uh, yes, Damocles, we're pretty much convinced that an atomic war will occur within five years or so. Keep an eye on these types of transmissions, they'll probably get very busy just before or after the war. And once the war has happened, if you haven't heard otherwise, send out signals like this to wake up some teams of Special Forces soldiers."
Which actually fits with canon -- after all, plenty of Morrow teams are depicted as being activated by Damocles. Why not some Snake Eaters, as well, with perhaps a more informative stream of information from the big ol' computer? Although, it's stated in the "Damocles" scenario that his knowledge of the Morrow Project is erased if he's restarted ... apparently he has very volatile memory! Probably just as well for the members of the Morrow teams -- otherwise within a few weeks or months after "getting into" the Damocles complex, teams of Snake Eaters would be arriving to ( a ) grab them and ( b ) restore Damocles to Federal control.
If you believe "nuclear war is inevitable within as little as five years", plenty of other actions are possible -- most of which don't affect the published game. Reviving the Civil Defense shelter programs; arms treaties with the Soviet Union; strategic missile defense systems; big ol' supercomputer in Michigan ...
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Michael B.