What potential chaleenges would the first female president of the US
face , related to gender. What is the general Job description of hte
US president ansd what issues would a woman have with these duties ,
due to her gender.

It depends on the woman.

I would have absolutely no confidence in Hillary Clinton but ...

Pinkfreud?

Wow, yes! I think that she would do a GREAT JOB!

Pink for Prez!

I shall not seek the presidency of the Probonorepublic. My
non-candicacy, as established here, stands:

http://www.answers.google.com/answers/threadview?id=328349

A less dexterous female President would have trouble using Urinal One,
the implications of which are chilling to say the least.

The present president looks like he does it sitting down, his wife
trained him before he gave up drinking   - and wasn't able to see
straight.  SO, we can leave that aspect of the question.

A female president would have to learn how to salute; 
she'd have to have a female press spokeswoman, one who was clever at
fielding questions about the media's headlines about her goings on
with:
1)  her husband,  or for lack of him  - or not;
2)  the Secretary of ..., ..., ..., ...;
3)  a member of her Marine guard;
4)  her press spokeswoman,
5)  Putin  - or any other head of state she met more that once (except
the Chinese),
6)  if R. Catholic, her confessor;
7)  the Vice President;
8)  (this is really still about the cleverness of the press spokeswoman)
    her perfume, hairdresser, dressmaker;
9)  what her husband does.

Actually, female heads of state have done quite well in other
countries and in international relations (well, Angie Merkel still
needs to prove herself).
Pink would do great:  extremely savvy; has an appropriate animal story
for every ocassion; speaks/writes so that she can be understood by
everyone  - without having to revert to the 200 word basic English
vocabulary favored by the incumbent.  The red hair could be a problem,
but can be fixed (see #8 above).