Also, can her nearest living relative get her death certificate for you? One of her children would be able to have access; privacy restrictions can be quite hampering. I don't know how many years Iowa (assuming she died there) makes you wait but 50 years will come around in 2016, not that far away.
Look in the Social Security Death Index (on FamilySearch) and apply for her original application for Social Security (assuming she made one).
Here's some "how-to" videos you may find useful.
This record provides her birth date, do you know where she was born? Is Schug a maiden name?
United States Social Security Death Index
"United States Social Security Death Index," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/JYYB-H53), Corrine Roseke, Mar 1966; citing U.S. Social Security Administration, Death Master File, database (Alexandria, Virginia: National Technical Information Service, ongoing).
Given Name: Corrine
Birth Date: 23 May 1923
Social Security Number: 484-28-2080
Event Date: March 1966