What did the error message say, was it just a friendly alert from the troublshooter icon to remind you - or was it one saying that a hard drive failure could happen soon?
If you manually make a backup using the "backup and restore" centre (just search for that on the start menu), then it should let you know how big a full backup will be, IIRC. The size could be anything, as if it's a full system backup it will compress everything on your drive.
Personally, I much prefer to use Acronis - it's much better than the Windows backup tool. That tells you how much space you'll need and it may even be a free download depending on what make hard drive you have got (Maxtor, Seagate and WD have a free branded version, I think). If your drive is by one of these guys, let me know which one and I'll find the link for you

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