How large is the destination drive? Perhaps its physically to big. TM should prompt you to delete Time Machine backups (though it never does for me), it will not prompt you to delete other files that you may have placed on the same drive.
How long have you been using TM? Could you have added a huge file recently? A movie or podcast from iTunes? You might just have to delete the file or exclude from backup.
Time Machine will _never_ delete the last backup (because that would put you at risk if something goes wrong during the next backup), so you need space for the complete last backup, plus changes that you made. Apparently you made an awful lot of changes - 328 GB worth.
To fix this without buying a new hard drive: Go into Time Machine preferences, pick folders with a total size of 250 GB and exclude them from the backup. Preferably pick folders with few very large files. Do a backup. Then add these folders back in again bit by bit, doing a backup each time.
This can also happen when a Time Machine volume or backup gets corrupted because of failed/attempted backups. I used to have this problem a lot with Time Capsule.
At that point, Time Machine tries to rebuild the initial backup again and if there’s not enough space to hold two full backups (the original corrupted one and the new one) it gives you this error.
The only way to recover from it is do what others have suggested and get your backup down to the available space or just wipe the Time Machine drive and start over.
If you need to recover files from the corrupted volume/backup that no longer reside on your current hard drive, you may have to do it manually through the Finder if Time Machine can’t mount the old backup.