Hi everyone,
I had the same problem and I eagerly waited for every iOS update to get it solved but nothing ever changed.
Then, I got it. And it seems to be extremely simple.
I can't say if it works also for you, but it worked for my Ipad, my Iphone and both my wife's Ipad and Iphone that had the same problem.
Basically the reason IS that the iOS update set the photo stream as automatic, and this will probably take too much space, but the solution is not just to turn it off, but you also have to do another thing that is to WAIT th right moment to do the backup.
Let's move to the solution:
go to SETTINGS->ICLOUD->ARCHIVE->MANAGE STORAGE
select "this iphone" or whatever device you're trying to backup
Now's the trick:
WAIT until "Backup Options" stops loading the size of the next backup. WAIT until "next backup size" is update with a number on your display.
Now, if this number is little enough to stay in the storage capacity you have, just go back to iCloud settings, choose backup and start the backup (remember to be wifi connected).
If the number is too big, just choose what to delete form next backup (your choice will probably be the photo stream...) and then wait for the new size of the "next backup" to show on the display. Go back and start the backup.
In short, it seems that if you don't let the device calculate the size of the "next backup" and show it on the display, the system won't be able to backup successfully.
I know it seems a stupid bug, but it worked for me.
If you still have problems with this issue, let's give it a try.
Hope it will be of any help.
cheers