There is a solution to this (described in http://pondini.org/TM/B6.html ) but I believe it only works under 10.7 or later operating systems and you are using 10.6.
Basically, it sounds like when you restored all your files from your backup to the newly formatted hard drive, Time Machine sees all those files as NEW or CHANGED because they are on a newly formatted hard drive and hence they all look different to Time Machine, even though their contents have not actually changed. So it wants to back them all up to the backup drive (again) and the only way to do this would require it to delete existing backups on that backup drive, including the most recent one, which Time Machine won't do. Hence it reports that there isn't enough room.
I suggest you purchase a new backup drive and start using that from now on with the newly formatted internal drive for backups. Alternatively, you can erase the external backup drive and tell Time Machine to start using it for backups, but I'm not comfortable with that because erasing your only backup seems unwise to me.
A new 2 TB external drive from Western Digital can be obtained for less than $100.