I installed Optifine, and disabled anti-aliasing in the Nvidia Control Panel. Then Anti Aliasing worked fine, well after I disabled fbo:enable. It seems like there might be something blocking the driver from Minecraft. Also, Mojang ignoring the posts and marking them as duplicates on their bug tracker isn't really helping much.
I just found this on Mojang's bug tracker page. Dinnerbone says he will be adding a native anti-aliasing setting. But that was from October 2013. I really hope this is still planned.
https://bugs.mojang.com/browse/MC-32275?jql=text ~ "Anti Aliasing"