If Trek history had any realism to it, the Americans would have murdered the Vulcans during First Contact and raided their technology ...
Would depend heavily on what part of America the Vulcans landed in, given tha they landed in the western section< I think what we saw is what would actually happen, the people around the landing site would introduce themselves and invite the Vulcan to socialize at a nearby cantina. Some drink, good music, a little dancing, and lots and lots of talk.
It goes without saying that no one would notify the government.
The government probably just screw it up.