System Information
Operating system and graphics card
MacOSX Version 10.9
Graphics Card: NVIDIA GeForce GTX 775M 2048 MB

Blender Version
Broken: 2.69.0 r60991
Worked: (optional)

Simply changing the Input type in Preferences to "Maya" and then saving "User Preferences" causes the object (that previously imported ok) to now fail on import into Unity.

Open a new scene, and use the default cube. Choose File -> User Preferences. Click on the "Input" tab at the top, then right below, set the dropdown box that defaults to "Blender" to now be "Maya" Next, click on "Save User Settings" at the bottom. Save scene somewhere so it can be used in a Unity scene. Open Unity, and drag this blender model into the scene, and it will say that it failed to convert the file into an FBX.

You might be thinking at this point that this is obviously a Unity bug (and it very well may be) HOWEVER. If you now go back into your same exact Blender scene, and simply set the Input type back to Blender, then save User Preferences, then save the file.....it will now load perfectly fine in Unity. Again, no changes to the model or anything else other than that User Preferences.

The reason this has come up is we're an educational facility for kids, so it's much nicer for them to use Maya's Input style since it matches Unity. But if the models don't import correctly, then we're kind of dead in the water in that aspect.

Based on a (as simple as possible) attached .blend file with minimum amount of steps. Please use the "default" scene.