Tangenting from a discussion as to whether naturalized US citizens ought to be allowed to run for President (which would require a constitutional amendment), Texas Law Professor Sandy Levinson asks whether originalists can even allow women to run for President. After all, "If one is an original intent buff, one might want to interpret 'he' in the Constitution as barring women from running for president, since it surely the case that no Framer could have envisioned any such possibility." Article II begins by using "he" to reference the President, but then shifts to the gender-neutral "person." However, I recall reading that in the early days of the Republic, voting laws that did not specifically restrict suffrage to men were still interpreted that way by the courts. And indeed, I believe in New Jersey an early suffragist tried to take advantage of gender-neutral language, but was arrested by the authorities and prevented from voting.
It does seem difficult to argue that the founders would have anticipated allowing a female President, given the retrograde views on women held in America throughout most of its history. No constitutional amendment has specifically given women the right to President. The 19th amendment did grant them the vote, but one can be franchised and still be prohibited from holding certain political offices (as are naturalized citizens).
So it's a difficult question. Are originalists committed to disallowing women from running for President? Does Hillary Clinton need to follow the same route as Arnold Schwarzenegger and get a constitutional amendment to take her shot at the White House?