Cannot download iOS7 on my iPhone 4S

When I go to the App store, I don't even see iOS7 for downloading. Under Settings (general), the phone indicates that a system update is available, but the phone itself does not indicate that there is a systems upgrade available (as was always the case for prior updates). I see that other people are having this problem. One response indicates that this is all the result of too many people trying to download the upgrade. Could it be that simple?

Just to be clearer, under General -- Software Update, the Upgrade option does NOT appear. It describes iOS 7.0 but does not provide a mechanism for installing it.

I think I've discovered the problem -- insufficient storage space. Just deleted apps, files, etc. and purchased more space. Still not able to download app, but will turn off phone and hope that the storage fix works.