I am pretty sure that it means "General Schedule". It is a way of ranking and classifying certain government jobs. They are titled GS-(a number goes here), and that allows information about the type of job, difficulty, and pay the person receives for such a job. However, this passage casually brushes by the depth of what a GS job is, and refers to the position Mrs. Kennedy is in after her husband dies. She doesn't have a job like the secretaries have a job, and the secretaries are given a GS title for their jobs. So, the passage was saying that there was no GS title for a widow.