iMac repeatedly asks for iCloud password

When I turn on (i.e., power up) my iMac, I enter my password and Yosemite boots up. All ok. I then immediately am prompted to enter my iCloud password. I enter the password by copying and pasting it from a password manager app (so there is no chance of mis-keying) and I click on Log In. At this point, the same window re-appears, asking me again to enter my iCloud password. I again paste my password and click Log In. This happens 9 times before iCloud stops prompting me. Anyone else having this issue, or knows why iCloud prompts me for my password 9 times?

After entering my iCloud password the 9th time, I then am prompted to set up app-specific passwords for FaceTime and iMessage. I previously set these up, so I just click Later. FaceTime and iMessage work fine on my iMac. so the "app-specific password required" message seems bogus. Any thoughts here as well?

FYI that I have two-factor verification enabled for my iCloud ID. Thx