The chair of the DNC is not (even a little bit) the leader of the party, and the Whip is not the person who determines what policy people are to be whipped to.
A sitting President is always the head of their party.
My understanding of US political parties says that they do not have a rigid structure nor a single head. Indeed if you look through the section on the structure of the Democratic Party on Wikipedia (see http://en.wikipedia.org/wiki/Democratic_Party_(United_States... - really, go look) you won't find Barack Obama's name anywhere in that section.
The President has a huge bully pulpit. He is in charge of one of the 3 branches of government. The public hears and sees the President.
A sitting President is always the head of their party.