Lets be thorough before you delete your data (data that iTunes is refusing to backup).
iTunes backups should be stored within a folder inside your user account…
~/Library/Application Support/MobileSync/Backup/
Try opening that location via 'Finder > Go > Go folder…', enter that entire path & hit return.
Get info on the Backup folder and double check that location is contained where you think it should be - the path should be inside /Macintosh HD/Users/USERNAME/Library/Application Support/MobileSync/Backup/
Do you also have read & write access to that folder?
You can erase the iPad if you think that is the issue, however I'm concerned that you are deleting data that may be important to you. An iCloud backup should allow you to restore the data if you can stand waiting for it to upload & download.
Personally I'd also contemplate creating a new user account (System Preferences > Users & groups) & backing up the device to that new user via iTunes - that would indicate your user account is flawed in some way.
Obviously if you haven't done so already, reboot just in case 🙂
Also consider booting into recovery mode to verify the disk in Disk Utility. It may seem like overkill but size errors can sometimes mask failing hardware errors.