Morgan,
In doing some research on this issue you are describing, I was able to find out, where this is a logged bug with development. I am including the bug number, title and its current status for you. Please let us know if you have any further questions or issues. Gracias, Morgan!
[#NIM059044 Error packaging a published map that contains some types of basemap layers. ]
Status:
New �?? The Nimbus bug/enhancement has been logged by ESRI Support and is in the process of being reviewed by Development