The size of your NANDroid backups is directly related to the amount of apps you have installed on your phone, and amount of data these apps store on your phone's internal memory. Even though CWM excludes the
/data/media folder (which is usually mounted as
/sdcard on newer Android OS versions,) the contents of
/data partitions alone will take plenty of space in the resulting backups.
Backup size of 2GB is not that uncommon, especially for phones without external storage. Consider an app like Google Plus, for example. The app caches articles and images from your stream into
/data/data/com.google.android.plus/cache directory. The more you use the app, the more this cache fills up, and the more space in the backup it will require. Same with other apps, like Google Chrome, or Gmail, for example.
To mitigate this, you can always clear the caches for the largest apps in
Settings -> Apps -> All -> Sort by size. Also, an alternative to CWM called TWRP recovery has an option to compress the backups in order to save on storage space. Some apps give you an option to store their data and cache onto external storage on phones that sport SD Cards (Google Play Music has such an option, for example.) NANDroid does not back up contents of SD Cards, so selecting this option will further shrink the size of your backups.
In terms of keeping backups on your phone, I would strongly advise against it. I usually keep only the most recent backup on the phone, and copy older ones to my PC. This way I have the backups in case the internal storage of my phone is rendered non-accessible.