Is this a stag beetle?
This is indeed a Stag Beetle (Family Lucanidae); in particular a member of the genus Lucanus.  Looking at the bugguide.net page for the genus here your specimen is most likely Lucanus capreolus, though Lucanus placidus also looks possible -- the two species are very close in appearance, though the former does seem more likely based on distribution.  Consulting The Generic Guide to New World Scarab Beetles here confirms that L. capreolus is featured here -- the femora (the first long segment in the leg, and the first we can see -- look at the right front leg) are bicolored (darker at the tips) -- the femora of L. placidus would be solid dark brown to black.