I'm not sure if this is true in your case, but I was under the assumption that all the contacts on my iPhone would be synced with iCloud. This is not the case (at least in my experience). Sometime in the past, I had added additional contacts from other sources to my iPhone. Those contacts aren't appearing in iCloud. In my case, these were contacts from Facebook, Outlook and Gmail. When I got a new iPad, I couldn't figure out why the contacts on my iPhone didn't match the contacts on my iPad from iCloud. Once I added the other accounts to the iPad, I was finally whole!
To add Facebook contacts: Settings > General > Facebook; Sign into your Facebook account and agree to allow the app to share contact information.
To add Outlook and Gmail contacts: Settings > General > Contacts > Accounts; Add the Microsoft and Gmail accounts and agree to share contact information with them.
Another note: The troubleshooting document, Get help using iCloud contacts..., mentions the Groups button in the upper left-hand corner in Contacts. This will not be there until you have contacts from more than one source/account. I was having fun trying to follow the directions, and the button just wasn't there until I added my other contact source accounts.
Hope this helps!