On the publisher's support page, the following Q&A is listed:
Q. Can I Log Into My Nintendo Network Account on a Different Console?
A: No, you cannot. A Nintendo Network Account can only be used on the console where it was created. In the future, you will be able to use your Nintendo Network Account with future Nintendo consoles and other devices, such as PC's.
This means that unlike the Xbox 360 and PlayStation 3 where user accounts can be accessed from any console, Wii U users will only be able to access their Nintendo Network ID from the Wii U that they originally created the account, at least for now.
It is unclear what Nintendo means when it refers to "future Nintendo consoles." Whether this means that the Nintendo Network IDs will be compatible with future consoles in general or future iterations of the Wii U is not stated on the support page.
Polygon has reached out to Nintendo to find out what happens to a user's Nintendo Network ID if their Wii U becomes broken or stolen and whether there are any plans to enable users to access their IDs from Wii U devices other than their own.