Ugh.. A couple of TERABYTES?
I think you need to look at another solution!
I do use online backup for my important files (Quicken, Word/Excel, Work Files) and my pictures (~15GB). I personally use "IDrive", and pay 50/yr for 150GB of space (with versioning, which is important to me on my DOC/XLS files). I'm pretty happy with it, and it does have a free trial, so I'd suggest you download it and take a look at the program to see if it works for you. The interface leaves a bit to be desired (why can't they just use something like BE/NBU??), but it does seem to get the job done!
A couple of TBs of data is not going to happen though (unless you have a T3+ in your house!). If you really need to backup that much data, I'd suggest you get a small RAID array, backup to that on a periodic basis, and send the array offsite (safe deposit box). Anything "online" with that much data is going to almost necessitate a T3 or higher connection.
Even with a 2Mb uplink (typical cable speed), you only transfer ~300MB per hour, ~6GB/day. It would take ~150 days per TB!