XNA Game Studio is not designed to work with the new Visual Studio 2012. I keep looking around for an update, or even plans of an update for VS 2012, and I don't see anything. In fact, this very fact has a number of people in the XNA world very worried.
But let me assure you that this is the same thing that happened when VS 2010 came out. It took them a while to make XNA Game Studio for 2010 versions. It took until the release of XNA 4.0 (maybe it was 3.0?) before they had it working. And until then, you were stuck using the 2008 versions.
So I'm not too surprised by this, but I'll admit it is a little frustrating. Especially with the lack of information about it.
Let me also add in two things that may be relevant. First, they have a tendency to spring things like this on us. Visual Studio Express 2012 for Windows Desktop was announced, but there was never any beta or anything. Just suddenly it was available for download. A similar thing may happen with this.
Second, the information I currently have is that they're planning on having far more updates to VS 2012 than ever before. Something along the lines of once every 3 months. So we may easily see this come along in a few months.
Having said that, last night I was playing around with this myself and I was able to get a game working (showing the CornflowerBlue background) in VS 2012. I took notes while I was doing this, and I'll post them later on. But the piece I have yet to get working is the content projects. And I don't know how easy that would be to do. It seems like it would require building a custom project type and installing it as an Add-In. Like XNA Game Studio is.
So anyway, I'll post what information I can later tonight or tomorrow.
I'd recommend sticking with VS 2010 (or Visual C# Express 2010) until they put out something more official. That's what I'm planning on doing, I think.