Unfortunately, I do not have a song or a video to lead you to as an example of current political euphemisms, but I will provide several examples and hopefully, they will be memorable enough for you to come up with some on your own as well.
Keep in mind that a euphemism is an appropriate (or socially acceptable) word or phrase that is substituted for an inappropriate (or possibly offensive) word, phrase, or idea. The term euphemism is most often associated with sexual connotation, thus, giving them the very nature of being considered generally negative (or inappropriate).
Politics is a great place to look for euphemisms that are meant to be positive. These euphemisms have become political "catch phrases" in our history and society that spark up around annual election times. Essentially, political euphemisms are those words and phrases Americans have adopted as being "politically correct." It is difficult to assert that there are no "hidden meanings" behind these euphemisms, however, as their purpose is to generally cushion a potentially unacceptable idea into one that is not only okay to think about, but to speak openly about as well. Notice the following examples:
"A chicken in every pot," or "A car in every garage." = essentially, these catch phrases were used to promote the idea that all Americans deserved wealth and success.
"Pro Choice" and "Pro Life" = these euphemisms have become completely acceptable and in fact, defining terms for the position an individual takes on what was once a socially unacceptable subject: abortion.
"Undocumented Workers" = has become the term for illegal aliens living in the US. This euphemism takes the negativity out of the term and suggests that despite the fact that this group of people may be breaking the law, it is acceptable for them to be here.