I can't think of Obama and Biden as Batman/Robin simply because I already consider them to be the perfect buddy cop duo.
Young idealistic by the book Obama. Old and cranky, foulmouthed Biden. Together they fight crime!
Seriously, Obama passes some new laws, Biden is heard commenting about how "[that] is a big fucking deal." Obama wants to make some changes to the gun laws, Biden calms down the second amendmend fanatics by saying that if Obama tries to take his Beretta he will get in big trouble with Biden.