Time Machine backup taking a loooong time, is this normal? I bought an external hard drive, plugged it into the USB port of my Airport Extreme base station, turned on Time Machine, set it to use that drive for backup.

It's backing up 350Gigs of data and it's literally taking days to work its way through.  

Is this normal? It seems like it's taking a way too much time.
350 GB is a lot of data, especially to transfer wirelessly. It will take a long time. In the future, only changed files will be backed up, so the backup will be much faster. To make the initial backup faster, you could try connecting the drive directly to the computer using the fastest possible port (see this question for a discussion of which ports are fastest). You will still be able to use the drive through the airport for future backups.