With the assistance of the earlier response, I was able to identify the exact cause of the same problem that I was experiencing. It is a known problem, and version 6.2 has a patch. Without a good stack trace, it may be impossible to determine whether the exception is masking a deeper issue. An alternative is to update your Entity Framework to the most recent 6.2 pre-release build, identify the root of the issue, and then downgrade to your current build, in my case 6.1.3.
At this point, you need to get a thorough error message outlining what went wrong and providing instructions on how to fix it. In my situation, a file access problem necessitated running Visual Studio as an Administrator.
When the problem is fixed, you can either go back and undo the modifications you made to the entity framework version or use the methods above to update to the previous version you were using.