Traditionally, whether presidents are portrayed as tough warriors or not, you'll see his soft side, but largely manifested through the largely different role of the president's wife. She'll have to have a husband, and chances are they can't present her as an emasculating wife.
The Glenn Close model makes the most sense a hard-assed, hard-nosed leader for a male-oriented group. It used to be that if a woman played a tough leader role, it was seen that she was not a woman, but asexual or gay.