A family I am researching fled Germany in the 1930s and settled in Illinois. In the ship's manifest, they listed one relative as a sponsor, but according to a member of that family, several sponsors were required. I am wondering if this sponsorship information is available somewhere, and, if so, how I go about finding it. Is it in NARA? In regional archives?
I followed up on @AmericanLuke's reference and sent a request to the Holocaust Museum for the source of their information. (To send them questions, use the Virtual Reference Desk form.) The response (just hours later!) pointed me to the United States Citizenship and Immigration Service (USCIS), which maintains a Genealogy section on their web site.
The USCIS can provide a range of genealogically-useful documents related to immigration and naturalization, including certificate files, alien registration forms, visa files, and other documents. The process for getting them is somewhat convoluted: you first have to order an index search for a specific individual ($20), and then use the results of this search to order specific files ($20 for documents on microfilm, $35 for documents stored as paper originals). Needless to say, it would be expensive to do extensive searching in this collection. On the other hand, judging by the description on the site, the visa papers are a treasure-trove of information, including details on the parents (such as the mother's maiden name).
Also note that if you request information on individuals who were born less than 100 years ago, you will need to provide evidence of death. The web site details what constitutes reasonable evidence, and things like obituaries and SSDI records are acceptable.