Mars Attacks!

If aliens landed on the White House lawn, the first thing we would have to do is pray they are friendly. If the alien race was intelligent enough to master interstellar travel and land on Earth, chances are they have some awesomely devastating face-melting death ray. But as Andrew said, it’s not conducive to assume they want to enslave us or sap our planet for resources, so for the purpose of argument, let us assume they’re generally peaceful, or at least didn’t come to exterminate the lot of us. Besides, I would assume that the development of interstellar travel would be so costly and consuming, it would require the cooperation of the whole planet, meaning they would have probably figured out peaceful solutions to the large majority of their problems (thanks Adam).
A definite possibility is that we go hostile first, assuming they are the aliens from the movies, here to enslave/consume humanity. In which case, the aliens turn on the death laser, there goes humanity. Or if we do something to provoke them, such as contain them to study or disassemble the ship without their permission, again, the death laser. The US would have to be very accommodating, and offer to show them our culture and whatnot. A peaceful exchange of knowledge would clearly be beneficial, considering they mastered interstellar travel and all. But I think we would probably shun the aliens simply because they’re aliens, and try to glean as much information and technology from them as possible, using probably most means available.
I think the proof that humanity is not a lone speck of intelligence floating around in a dead universe would unite humanity. As the world has shrunk due to increased mobility and technological advances, and people have united under larger groups. People have identified themselves as members of the city they were from, and then a larger region, then from their country, and now in some cases their continent. The knowledge that there is a massive empire of intelligent beings elsewhere in the galaxy would cause people to unite and think of themselves as citizens of earth and humanity.