Hey rdharles,
The reason why its not working for you is because the services you're trying to use are "Feature Services".
Try publishing or selecting a mapping service and then using it as a basemap.
Basically avoid services that have "(Feature Service)" appended to their names.
Hope this helps,
Nelson
Good to know, appreciate the response!
The layers in "My Content" were created in two ways, both built from shapefiles.
1.) Feature Services were created inside of ArcGIS Online my uploading a zipped shapefile.
2.) Web Services were created by using ArcMap 10.1, doing File > Share As > Service...
Not sure if you can create a "Web Service" within ArcGIS Online?