I use Windows with Skydrive backup, same concept as Time Machine. Great for gigabytes, but as you've found all these solutions aren't tailored to terabytes yet.

If you're looking for a grab and go solution for 2 TB of data I'd recommend running a Network Attached Storage (NAS) device with ejectable drives, those scale up to 3-8 TB right now. I have one of those running now for video and archival purposes, 3 TB capacity (actually about 2.2 TB I think) in a RAID configuration: if I had 5 minutes to 1 hour to evacuate my home I could eject the drives and conceivably carry the data with me, if I wanted it. Frankly its not in my plans, like others I have my vital stuff in the cloud and am happy to kiss goodbye the copies of TV and film which make up most of the terabytes I have. Its just stuff, and I'm pretty sure I could find copies of Duck Dynasty if my NAS device were to disappear.

EDIT: Some other posters have touched on data security, I use Win7 with Bitlocker drive encryption on my work devices (desktops, laptop, Windows Phone) admin'd by my employer and run my own Bitlocker on personal PCs - why let the scum that steals your PC have access to all your data. Encrypting your cloud backup can work, mebbe - for me a better solution is to scan and put my most important docs on redundant thumb drives and put them in my safe deposit box. Twox4 GB thumb drives cost about $40 for what I consider to be the more reliable types (Lexar, Kingston), and my important docs don't change often.