It's most likely a validation error. Basically, what's probably happening is that the NOAs haven't uploaded the database of registered usernames and passwords, so it is trying to check your username and password with a database that doesn't exist--hence the error.
If you want a more detailed explanation, I can give one.
It will be fixed whenever the NOAs upload the database of usernames and passwords to the server, which will most likely be soon. It won't mess up the Camp Hyrule schedule of events, so don't worry, and just relax and have fun until it's fixed.
^_^
Edit: Oh, and no, no one can log in as of now. And no, the server won't become overloaded. A major corporation like Nintendo has multiple serverside machines that distribute the traffic between them to reduce server congestion.