Asking Hillary to head the State Department might create some headaches for Obama, but could help him in at least one extremely important way: by giving him cover to appoint Larry Summers as Treasury Secretary.
As Jon Chait notes, some feminists are already pushing back against a Summers appointment--saying impolitic remarks he made while President of Harvard should disqualify him for the job. But if Obama announced Hillary will be Secretary of State and then appointed Summers, it would surely take away some of the sting.
That would allow Obama to head off a resurgence of the identity politics that paralyzed Bill Clinton's first term, while simultaneously putting the best economic mind available in charge solving our most pressing problem--the economic crisis. As an added bonus, it would keep John Kerry and Bill Richardson from heading up the State Department.