If the packaging failed, it's best to check the GP Results windows for additional information about the error. If error lead you to believe that Desktop cannot connect to the server, try running Fiddler to see if you can find the failed request to the GIS Server.
On the server side, you need to make sure the Publishing Service is running. It's also good to test your publishing as the Primary Site Administrator to make sure it's not a security configuration issue.
If anyone in the thread reporting these problems is experiencing them today, please contact Esri Support so an analyst can help diagnose what the problem is.
Thank you,
Andrew