Legally, a woman can't be elected president

Most people believe not only that the 19th Amendment permitted women the right to vote but that since women serve in Congress, the courts and other offices of government, the office of president of the United States has been de-genderized.

Not true. This important legal question exists now and has not been constitutionally addressed. The language and syntax of the 19th Amendment merely removed the barriers that prevented women from voting. It did not identify women to be qualified to become elected president.
http://www.cmonitor.com/apps/pbcs.dll/article?Date=20080220&Category=OPINION&ArtNo=802200400&SectionCat=OPINION02&Template=printart

Nineteenth Amendment to the United States Constitution
The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.
Congress shall have power to enforce this article by appropriate legislation.

http://en.wikipedia.org/wiki/Nineteenth_Amendment_to_the_United_States_Constitution