As pvonk says, probably you don't have enough space on the iPhone itself. I had the same problem. I deleted all backups in iCloud, leaving me with 5.0 Gb free space. The iPhone complained about "not enough storage". I turned off the photo roll (3.6 Gb) and ALL applications data, leaving me with a backup of only 76 mb. STILL, it didn't want to backup.
I looked in the Settings>General>Usage> and could see I had around 5 Gb free disk and 7 Gb used, which seemed pretty good to me, but appearently not. What FINALLY solved the problem was that I deleted some movies from the camera roll, around 1 Gb. Now, suddenly I could do the iCloud backup with the camera roll and all application data.
(N.B. The total backup is below 4 Gb, so it really wasn't a lack of space in iCloud.)
Apple's crappy error message just couldn't tell where the real lack of space was.
3 hours of my life wasted on bad user experience. 😠