Now, I've been one of the louder advocates about switching to Battle.net account amongst my guildmates and the other WoW Insider writers, I absolutely think it's a great concept. Just as I fully support Steam, I support any Steam-esque services of a decent quality. This here? Quickly losing my favor. If the error message above is truly what it implies, that the login server is failing due to heavy traffic, I must repeat what we've said the last dozen times something on Blizzard's end has fallen apart due to too much traffic: Come on, really? You underestimated your service's popularity? Again?
If there are any further chapters to this story before it's fixed this evening, we'll be sure to let you know.
Update: The error is getting more sporadic as the night wears on, so I'm personally going to assume that it is, indeed, a traffic issue. None of us know that for a fact, of course. Still, if you try now, you'll have better luck getting in than you did a short while ago.