Web deployment task failed. (Connected to the remote computer ("waws-prod-blu-003.publish.azurewebsites.windows.net") using the Web Management Service, but could not authorize. Make sure that you are using the correct user name and password, that the site you are connecting to exists, and that the credentials represent a user who has permissions to access the site. Learn more at: http://go.microsoft.com/fwlink/?LinkId=221672#ERROR_USER_UNAUTHORIZED.
One thing to remember is this, on the Dashboard of the web site, you will find
DEPLOYMENT / FTP USER
But when filling the Visual Studio Publish Web Dialog, in the user name field do not use website name as prefix.