My other streaming ways are working fine. Youtube works, all Wii U online features work. I get an error message even before the list of movies pops up.
I contacted Netflix support (got a local guy, and we even chatted about the Wii U for a few minutes) but we weren't able to solve it. He's going to create a help ticket for my case and contact me from around 4 to midnight tomorrow.
Also, I found out that you can use press up, up, down, down, left, right, left, right, up, up, up, up, up for a debug mode type thing with your account and system info plus another way to deactivate Netflix on your system. Pretty neat.