This is a reference to a <a href="https://en.wikiquote.org/wiki/Ginger_Rogers">quotation</a> about <a href="http://www.imdb.com/name/nm0001677/?ref_=nv_sr_1">Ginger Rogers</a>, who appeared in several films dancing with <a href="http://www.imdb.com/name/nm0000001/?ref_=nv_sr_1">Fred Astaire</a>.

Fred Astaire was supposed to have a reputation as a better dancer, the comment on that in the quotation was that:

> "She did everything that he did, but backwards and in high heels".

Referring to the fact that the man always leads in dancing.  She was suggesting that the woman has to work harder to keep up. 

The Obama reference using that quotation is suggesting that women have to work harder to keep up in the world of politics.