I'll try clearing some space to see if that helps. Thanks.

EDIT: I can actually see a progress bar for the download now, so hopefully that did it.

I actually had enough space, but it wouldn't start downloading until I cleared up some more. 

The game needs about 1,4 GB of free space. 
If you have this much free, than its most likely a server problem. If so, try to download the .obb files manually...  Or wait until the server is back to full performance.

You're probably out of storage space. The file is actually quite big IIRC

For several days, I've had a notification with the download icon saying "Additional file for Grand Theft Auto: Vice City." I've tried rebooting, canceling the download and starting over, and trying a better internet connection. Nothing has helped. Has anyone else had this issue?

I have an 8gb wifi Nexus 7. 

GTA:Vice City is taking forever to download