I believe that I have found the most likely parent for them.I believe his father is James in Greensboro, Greene, GA.In the Telamon Cuyler Collection, Manuscript #1170, Call Number: Box 42, Folder 2; Page Number: 1; Family Number: 45 at the Hargrett Library at the University of Georgia [online] is a petition signed by James Washburn.
Southeastern Native American Documents, 1730-1842 Summary: This document is an undated petition from the inhabitants of Greensborough (Greensboro), Greene County, Georgia, to Georgia Governor Edward Telfair (1786-1787, 1790-1793) asking that Telfair send arms and ammunition for the establishment of a fort in the county. The petitioners allege that Greensborough (Greensboro) is at increased risk for Indian attacks because there are a number of public stores in the vicinity. repository: Hargrett Rare Book and Manuscript Library, The University of Georgia Libraries.
This is about the time Samuel was born in GA.It makes sense as Samuel's first son is James and his brother is James.