I am having the same problem, starting today (12/15). Here's a more complete description of my problem.
About two weeks ago, I changed the email address associated with my Apple ID. The old address had been taken over by spammers, so it had to go. I followed the procedure in Manage My Apple ID, and everything seemed fine until today.
I am running Yosemite, 10.10.1 on an elderly Macbook Pro (2009)
I got a message saying I couldn't access iCloud and needed to log in in System Preferences. I tried logging in with my then correct password. After 3 tries I was locked out and told to use iForgot to reset my password. I used my recovery key and reset my password "successfully". My new password allows me to log into iCloud.com, iTunes on my Mac and on my iPhone 6, I am able to use my iCloud keychain on both devices, and I can log into Manage My Apple ID with the new password. I was also able to use the new password to log into iCloud on my iPhone. Access to iCloud drive from Pages appears to be working on my iPhone, but not on my Mac. I was also able to sign into the App Store on the Mac.
However, in System Preferences, I cannot log into iCloud and I cannot log into my iCloud mail account (both appear to use the same login). I get a message saying I have been blocked for security reasons and I need to reset my password. This is exactly the state I was in when I went and changed my password so it appears that the change didn't get communicated to system preferences. Without iCloud access, my apps that use iCloud for storage and/or syncing with iPhone apps are of limited usefulness. This may be key to the problem or at least a clue: System Preferences still thinks my Apple ID uses the old email address not the one it was changed to. The only way I know to change the address is through Manage My Apple ID
I tried rebooting by doing a full shutdown and restart, but it did not help. I also tried cursing at my Macbook but that did not help either.
I can use iCloud.com for mail and Documents since it recognizes my password. But this is at best a temporary work around. I'm off to check other sources for help. I'll report back when I know more.