I figured out the problem. EntityFramework.dll needed to be in the GAC for Visual Studio to use it from the package manager.
- Start Visual Studio Command Prompt (ensure you started Visual Studio as Administrator)
- Go to your packages directory and find the EntityFramework package directory.
- Go to lib\net45 (if targeting 4.5)
- type: gacutil /i EntityFramework.dll
- Restart Visual Studio
Note: It may be wise to restart the computer entirely at this point.
I'm not sure why Visual Studio stopped seeing the DLL, but this got me past this problem.