The project you are trying to open is a Web project. You need to open it by specifying its URL path.
I got this by pulling down the source for my project from a previous labelled version in VSS. We needed to implement a QFE to version 3.2 while we were working on 3.3, so I deleted all the source files on my drive and pulled down the 3.2 code base. The problem turned out to be a missing .webinfo file, which isn't stored in VSS (and shouldn't be, so don't do it!). I could have either used a copy of the file or wrote another one, but either way, the solution file pointed to the project (.csproj) file, so why would VS complain? WTF? Anyway, if you need to write a new one, assuming your project is named, WidgetManagement.csproj, the contents would look something like this:
<VisualStudioUNCWeb>
<Web URLPath = "http://localhost/WidgetManagement/WidgetManagement.UI.csproj" />
</VisualStudioUNCWeb>
Stupid, flipping Web projects!