I finally got it to work.
Here are the steps I took.
1. On your Mac, make sure all calendars are stored on icloud.
http://support.apple.com/kb/HT5029
2. On your iDevices, go to Settings - > Mail, Contacts, Calendars
Here you will see your main account that accesses mail, contacts, bookmarks, etc.
Any other accounts will access mail only.
3. Scroll to bottom of list - > Add account - > Other
4. choose Calendars - > add CalDAV Account
5. Enter Server name
(if an iCloud account, just put me.com. This is where I was stumped for awhile)
Enter user name, password, and description. This creates a new calendar.
6. On your iDevices, go to Settings - > Mail, Contacts, Calendars
Check to see if indeed you have another account that is Calendars, Reminders
7. On your iDevices, go to Calendar app
Show Calendars (a list)
8. On the main calendar, clear checkmark from previously subscribed calendar.
(this eliminates viewing duplicates and entries that do not update)
9. On the next calendar below (in the list), put a checkmark next to your new one.
Remove other checkmarks in the list from ones you do not want.
The calendars should now update automatically.
(My iPad updated almost immediately.
My iPhone took longer but did do it eventually.
You can always check iCloud storage to force refreshing sooner.)