So I had this exact same problem and the short story is that it is likely caused by corrupted sectors on your hard drive that are affecting your iPhone backup image. I ran Windows' CheckDisk utility and it repaired a bunch of bad sectors and then this error message went away allowing me to successfully restore my iPhone backup via iTunes.
Here is the longer story:
1) I went to do a backup via iTunes and was prompted to install an updated iOS version, so I clicked OK to proceed.
2) iTunes (fortunately) backup up my iPhone prior to doing the iOS upgrade.
3) The iOS upgrade failed with some error that I don't remember, but I now know it was probably caused by a flakey hard drive.
4) iTunes tried to restore my phone but the restore failed with the error about not enough space on my PC's hard drive.
5) This error about PC hard drive space not being enough made little sense to me given that I'm trying to copy an existing backup over to my iPhone, so why should I need more hard drive space if the backup already exists? Anyways, I went ahead and freed up over 200GB of hard drive space and I still got this error when trying to do a restore.
6) I called Apple Support and they had me try a bunch of things to no avail
7) As a last resort, I tried running Windows' CheckDisk Utility on my PC hard drive, it found numerous bad sectors and some were in the Roaming/Apple Computer/MobileSync/Backup directory where Apple stores your iPhone backups. Amazingly, CheckDisk seemed able to repair these bad sectors despite my having Symantec full disk encryption enabled.
8) I tried doing the iPhone restore again with iTunes and it worked this time! No more error about not enough space and my iPhone seems to work fine now with all of my pictures and content fully restored.
I think this error about not enough space on your hard drive is misleading, in reality it can indicate that something is wrong with your iPhone backup image (or maybe even the iTunes application image). Hopefully a checkdisk or even copying the iPhone backup image to a different computer with a fresh iTunes installation could help. I would suggest copying the backup to a new computer or another hard drive prior to running checkdisk just in case the checkdisk makes things worse or fails. Bad sectors are an indicator that you hard drive is starting to go bad and could fail any time.