It will be difficult for her and her publicist to repair the image because there may be no phrase that irritates the common person more than "Do you know who I am?". I participate often in a social network for very frequent flyers of American Airlines. The board has five open threads with DYKWIA in their titles. Invariably each anecdote originates with a high-profile passenger, typically a CEO or celebrity or politician, whose bad behavior is further tainted by uttering the arrogant phrase. The Delta board even has a standing thread entitled "'Do You Know Who I Am?': The Definitive Thread of DYKWIA Stories." There are over 2000 posts in that thread, as of today. Good Lord.
Perhaps you remember the late Leona Helmsley, at whose trial for tax evasion there was sworn testimony that she had said "Only the little people pay taxes." I am not suggesting that Witherspoon is as bad as Helmsley, whose conduct earned the epithet Queen of Mean. My point, however, is that even someone as apparently innocuous or virtuous as Witherspoon can be seduced by her own misunderstanding of herself and her place in the world. Without a doubt I am occasionally guilty of hubris myself, but I try hard to embrace humility. I wish that everyone would. If you catch me in a moment of hubris, call me out.
Final point: the Witherspoon incident reminds us that alcohol brings out the very worst in some people.