Quick hint: if you’re having trouble getting wireless backups on Time Machine and an Airport Extreme working, then try this – I had the same problem and fixed it for me. Plug the USB drive in to your Mac and using disk utility, veryify and repair the disk not the actual partition. Alternatively, remove all existing partitions from your drive, and then recreate the necessary partitions for your backup scenario. It seems that if you only verify / repair the partitions then the Airport Extreme won’t necessarily mount the drive properly (meaning you can’t use it as an Airdisk, and you can’t use it with Time Machine.)
No guarantee this will work for you and also note: wireless backups create sparsebundles (as opposed to real actual files) so it’s more of a headache to restore from a backup. But wireless backups are far less of a headache than having to periodically plug my Macbook Pro in to the drive, so for me, it’s worth it.