Not 100% sure on GSP (there are a few posters on here from there though), but it seems a pretty small airport with not a ton of traffic. Given that I'm guessing there won't be much wait at security, I'd aim to be pulling into the parking garage at GSP about 45-50 minutes before flight. Given that all GSP-ATL are now on CRJs, boarding doesn't really start until 20 minutes before departure, so it shouldn't be a huge issue.

My advice is to take a look at how many other flights are leaving around the time yours is. Just taking a quick look, it appears that there's a 1248p CRJ to ATL, a 1230p CRJ to DTW, a 1210p CRJ to ORD and a 1255p CRJ to CLT - otherwise, not a ton of traffic. Shouldn't be an issue.