It's Tuesday, which means maintenance -- or in this case, post-maintenance -- server problems. At present, @BlizzardCS says login issues for North American realms are under investigation -- though they may already be starting to clear up. If you manage to get into the Battle.net launcher, it will helpfully inform you: "Login to the Battle.net desktop app is currently unavailable. However, you can continue to use Battle.net in offline mode to launch and play games that are available offline."
I guess that means tonight's Diablo 3 rift runs are going to be replaced by Diablo 2 leveling.