I found this thread on the Microsoft SSIS forum that seems to answer all my questions:  http://forums.microsoft.com/MSDN/ShowPost.aspx?PostID=1748534&SiteID=1

Bottom line: Data Sources can be considered nothing more than a convenience provided...

Instead of creating multiple OLE DB Sources and trying to merge the results using transforms, I created a single OLE DB Source and wrote the SQL to do what I...

Thanks, I understand how that works in a SQL statement.  However, there doesn't appear to be a SSIS transform called "Union".  Merge doesn't appear to do what I want either. ...