Which database were you trying? There are four possibilities at ancestry.com:
Historical Newspapers, Birth, Marriage, & Death Announcements, 1851-2003 (includes Atlanta Constitution)
The Atlanta Constitution (Atlanta,
Georgia)
Daily Constitution, The (Atlanta,
Georgia)
The Constitution (Atlanta,
Georgia)
(These cover different dates, too.)
I tried searching for
Smith in the second one, and got over 57,000 hits. Maybe the system was "down" when you tried....?