Considering your clarified question, I'm going to address the main points of what the likely US response to this situation would be in a world with a similar political situation as we currently have.
Keep it secret - yes, it seems like a cliche, but it is that way for a reason, and this specific situation gives more reason than ever to keep the contact secret. Since it was the government that discovered this, releasing the information would lend credibility to other conspiracy theories much more so than if contact was made openly. Many would assume stories like Area 51's crash were true all along. Further, there is little benefit to telling others, since this contact could be strategically useful.
Maintain peaceful relations - despite what many think, I very much doubt the initial response would be to attempt to attack. There isn't much benefit and much risk to antagonizing them. I would point to a situation like North Korea, where there is proven and serious threat, yet the risk is too high to do anything about it. We have not even invaded Iran, where the risk is substantially lower. Attacking another planet would be incredibly costly, difficult, dangerous, and offer little in short-term reward. Aliens with weapons we don't understand would be North Korea to the nth power. No country on Earth would attempt to attack.
Try to get information - the main goal in this context would be to get their technology, both to even the odds with the aliens themselves, and to improve the US' standing on Earth. Without knowing more about these aliens I cannot say what this part of the response might entail, but it is easy to imagine the US government would do almost anything to get the aliens' technology. Think of what we have already done for technology boosts: unethical experiments, letting Nazis off the hook...
Try to use aliens against Earthly enemies - wouldn't it be nice if Marvin the Martian just zapped Putin into not existing anymore? Maybe Kim Jong Un? If the aliens could be motivated to take the US side in Earthly politics, they would certainly be pushed towards it by the US.
This would be the short-term response. In the long-term, the government would have to recognize the existence of aliens, and the amount of technology/intervention could make that sooner or later.
From that point, what would happen depends more on the aliens than on Humans. If the aliens are peaceful themselves, some sort of trade seems likely, and Earth might end up part of whatever power they are a part of. It depends greatly on the size of the technology gap.
If they're warlike... this whole question might not be valid, since if they attack first, there isn't much room to respond.