I think I found the answer. I had to modify my @Resource annotation to include the mappedName. Thus, it looks like the following:
@Resource( mappedName="java:/WebServiceContext" ) WebServiceContext wsc;
Now that I have that, I am receiving a different error in the server.log. This time it is making reference to "mapped-name is required for org.apache.cxf.ws.rm.RMManager/bus". I don't know where to put an annotation for that. Anyone know what I am missing here?