I can send you general information regarding Smithsonian internships.
While most internships here are unpaid, there is a chance that the
department which selects you will have money in their budget for an
intern.  You can also apply for a predoctoral fellowship through the
Office of Fellowships and Grants.  If you would like more information
give me a call at 202/357-3102.
 
Rebecca Culpepper
Office of Museum Programs
Smithsonian Institution