"she catches the eye of a gentleman from Chicago who makes sewing machines"

Whilst the most obvious link would be with the Singer Corporation, maker of striking sewing machines since 1851, their work was never based in Chicago but began in New York City.  The President of the Singer Manufacturing Company from 1889-1905 was Frederick Gilbert Bourne, married only once and also of New York.  

Another possibility was Richard W Sears, for whom the Sears Tower in Chicago is named.  His company, originally called Sears Roebuck Ltd, began with the production of watches and sewing machines before moving into retail in Chicago.  Sears lived from 1963-1914, but like Bourne he was married only once.

The president of the Free Sewing Machine Company, based in Chicago, was William C Free,  but I can find little information on his personal life.

Any suggestions as to who Carter may have in mind would be gratefully received!