TJ would be a comfortable guess. I don't think she is a ENTJ because she doesn't seem natural. ENTJs due to being extroverted with tertiary Se have a socially comfortable, natural, flamboyant vibe. She she is quite old it's safe to say that her tertiary function (which is Se if she is a ENTJ) would have developed by now. She doesn't have that vibe. I would go with ESTJ over ENTJ if it's between those two types.
However, it is possible she is an introvert. Now things get harder to type. But INTJs - all INTJs I know who are MALE - have a emotionally closed off, yet competent vibe. They are NOT even a quarter percent socially comfortable as their extroverted counterparts but they have that inner competence of adjust-ability that helps them SURVIVE social situations. Technically they should suck at it but they don't. BUT then again at huge, long campaigns such as an American presidential campaign they might crack and show that they are uncomfortable from time to time. Anyone would, even an ESFJ.
Hillary seems like she has been dragged out of somewhere and put in a place she doesn't want to be in. Does this mean she is an introvert. Not necessarily, perhaps she is a ESTJ. ESTJs though love socializing are NOT good at adapting. You could clearly see when they are uncomfortable and agitated. It's like they don't even want to try. 'Undisciplined kids' get out of my way is written all over their faces.
I would go with ESTJ and the second choice of INTJ.
Anyway, I hope she would be a good president if she is elected.