Q: Backing up new iPhone with iCloud data

Hello there, winbig2015.

The following Knowledge Base article offers up some great pointers for troubleshooting the issue you're describing:

Get help creating an iCloud backup

http://support.apple.com/kb/ts3992

I can't back up because there's not enough storage available.

If your iCloud storage reaches its maximum capacity, you can take any of these actions:

• Upgrade your iCloud storage plan.
• Create a smaller backup:
  • Select which apps to back up. Include only the apps that contain important data.
  • Delete unwanted photos and videos before backing up. You can also save the photos and videos to your computer before deleting them.
  • Turn off backup for Photo Library (or Camera Roll in iOS 7), especially if you already back up your photos to your computer. (My Photo Stream isn't a backup of your photos.)
  • Delete old messages from your device, especially messages with attachments. To delete a message, swipe over it, then tap Delete.
• Delete items that you no longer need from iCloud. You can save them to your computer before deleting them. For example, you can:
  • Delete old backups, such as backups for devices you no longer have. 
  • Delete app data or documents.
  • Delete old email messages, especially messages with attachments.

Thanks for reaching out to Apple Support Communities.

Cheers,

Pedro.