I was/am having the same issue once I upgraded to 10.1 sp1. I cannot right click on a layer in the TOC and export to the default.gdb. I can export to any other file geodatabase or sde. It just doesn't work for the Default.gdb.
Then just for giggles, instead of exporting to a folder connection that goes directly to c:\documents and Settings\<bubbastudwarrior>\My Documents\ArcGIS, I went to a folder connection mapped to c:\ and navigated to the ArcGIS folder with the Default.gdb and it worked. Go figure?
I don't know what is going on but this new "feature" sucks.