During a recent interview, Maxis general manager Lucy Bradshaw said it would be impossible to play SimCity offline without a significant amount of engineering by the design team as the game offloads a large amount of calculations to their servers so the computations aren't being performed on the local PC.
According to a recent post on Reddit by a modder named UKAzzer, however, that's not entirely accurate. He explains in the post how he was able to gain access to the game's debug mode. From here, UKAzzer was able to disable the game's disconnect timer which allows you to play offline indefinitely as shown in the video below.
He was also able to get rid of the fluffed population count and show the real numbers - a common complaint among players since the game launched more than a week ago. What's more, he was able to edit the highways anywhere in the game, even outside of your own city boundaries. Edits are reportedly saved even if you log out of the game then return. This proves that highway editing would easily be possible in the "main" game.
There are a few drawbacks to this method, however. Although you can play indefinitely offline, no saves/syncs or region related stuff is possible just yet but the simulation can carry on without an active connection which pretty much debunks the claim from Maxis.
In the meantime, EA has launched a SimCity Server Status page and issued a patch that claims to fix an issue that causes the game to crash. A recent post on Maxis' blog said they will continue to optimize and improve the experience moving forward.