Update (9/12/2012): Good news: Visual Studio Express 2012 for Windows Desktop is now available (here), and it supports NuGet out of the box. Generally speaking, every edition of VS2012 now supports NuGet, so this limitation should be a thing of the past!
Original answer:
Microsoft signs NuGet in a way that allows it to work with VWD Express. Ideally, it would also be signed in a way that it works with C# Express (it may have to be a separate build). Unfortunately, we were not able to do this for the initial release (it’s more of a challenge than you might think).
Going forward, we will try to enable this scenario. Feel free to file a bug on the NuGet site just to let others who are affected a chance to vote it up!