It might be something related to browser cookies. I went into Chrome preferences, cleared all apple-related cookies, refreshed the browser and tried to logon again. Worked for me right away.
Curiously, after the problem was solved in Chrome following my cookie-clearing action there, I had no further problem (even without clearing cookies) in Firefox or Safari (both of which had previously failed with the same time-out problem). So I now surmise that the problematic setting was not so much in a browser cookie as in some other apple-related pref file somewhere that was reset as a result of the Chrome cookie-clearing.
Then again, it might just be a coincidence that whatever it was went away at the same time I cleared Chrome cookies. I have no way to do further testing now that the issue is gone. So good luck!