This is a direct reference to Hillary Clinton. The genesis of the word-phrase comes from 50s high school talk, a time when bouncing blonde bimbos were unaware of the fact that the word whore
began with a W. Thus, one would overhear in the hallway, "Look at her, the little H!" So, ultimately, Hillary has come to fulfill the the void, The H. No doubt, the Republican Party will soon seize upon the phrase in a nationwide whispering campaign to their party workers to use "The H" when they refer to Hillary Clinton in public places.
I flipped on the tube and there was The H, giving Rumsfeld nine kinds of hell.