I think it will benefit both the American public and the Obama campaign, and I'll start from the skin deep reasons:
1) I think pretty young women are like precious artifacts – you seem to benefit from their mere existence – they make you happier. I smiled when I watched it and it made me smile to the next person I met and so it makes everyone a bit happier and this is a clear benefit. I guess the pope or certain Moslem clerics wouldn't agree with me on this specific video, but I doubt if sins are really done because of such videos.
2) Obama is a politician and for politicians there is no bad publicity, only publicity or no publicity (which is bad).
Now for some deeper thoughts: I think what she did there is accurate art in a profound way. She conveyed the notion that we look at our modern kings as celebs, as people to gossip about in our giant village where we are all anonymous. This thought is disturbing because our king can send us or our children to die for causes, can take away our bread, etc. only that our king is no more then the British queen (god shave her) because we have taken most of the power from our political rulers and transferred it to the money owners, thus making a move towards Greek democracy, in which only the reach men would vote, but all of them would vote (instead of selecting a king). So in our modern democracy the politician tends to become a representative image, a form for an a-morphed father figure, a metaphor if you will. This is exposed in the way she relates to him, like a teenager in love, not like someone dealing with the exchange of power and not like someone dealing with the king of all kings. Mind you: the reason that this video became important is that people liked it - it exposed what they thought, it was accurate for a lot of people.
It will help Obama exactly because of that. We do not need a Napoleon to lead us. The age of the great leaders (dictators) is gone. We need a face to love and an image we can identify with. The actual deeds will be dictated by public opinion, communication and corporate pressures anyway. He will not lead us, at best he will be led by us and realistically he will be led by pressures from corporate CEOs. An example for this is Clinton, who gained popularity after the public heard that he earned the affection of yet another young woman – this is exactly what we want.