edited to assist the good folks at Apple.
I had that issue about a week ago on a Sunday and I called Apple.
I am on 10.10.3
After a few hours in an Apple Session Key we tabled the issue and I waited to hear back.
Had time again last night to try to tackle it again with the folks on line with a Session key.
After two different attempts and 2 Level 2 support folks, I ...... put my thinking hat on.
Calling again last night (the third Session Key) and "starting over" with a new Level 2 Support... I led him along the path with the problem and we finally (well mostly me......) finally identified the problem. We did do the google account removal and reapply as well - that dd not fix my problem.
We isolated the problem to having 10,147 contacts.
We proved when I disabled the iCloud contact sync, and removed the contacts in Contacts (Addressbook), FaceTime worked. I believe Facetime "remembers" the 4 contacts I use for Facebook so I was good there. As I only use 4 contacts or so in FaceTime, it seems when FaceTime boots up, it preloads (or at least tries to) load all 10,147 contacts.
This method makes it easy to type in a name to find their FaceTime info so you can load them into your FaceTime contacts.
I think..... that Facebook has a time out feature that bounces until it times out. It should bounce until it loads all the contacts.
Simple to fix, just change the bounce criteria from a timed / timeout criteria of 132 seconds to a question of "Are you still loading? - Yes / No".
If Yes, then keep loading and bouncing. If No, then load the program.
If all contacts are loaded, then complete the load of the program.
Unfortunately, there is no way to disable Facebook association with all the contacts.
Unfortunately, you can not "just use your four contacts" alone.
FaceTime seems to always associates with all my contacts.
Checking again last night..... I proved this out with the Video/Audio tab in FaceTime.
While Video only displayed the folks I did FaceTime with, the Audio tab showed all 10,147 contacts.
So.. at this point in time, FaceTime does not work unless I disable contact syncing, they whole point of purchasing an Apple Macbook Air and a 5S.
Interesting Note, my wife has the identical setup and hers works perfect. She has 50 contacts.
Investigating deeper there is no published limit to the "Contacts" that I could find.
Anxiously awaiting to hear back from Apple.
Yes I guess I would be a beta tester for you folks. I think I know enough now on the problem to assist you folks.
See case AppleCare Case 789760242
Frank in Antioch, IL