Research indicated that the proper solution was to enable Kerberos and make sure that the servers and accounts invloved were setup properly for delegation, and that the correct SPN's existed. For a variety of reasons, this was not possible and I needed to find a way to resolve the issue outside of Kerberos.
The work around was to configure the Reporting Services integration in Cemtral Administration to use a Trusted Account rather than Windows authentication. Here's the steps needed to accomplish that:
Open Cntral Administartion and click General Application Settings:
Next, change the Authentication mode from Windows Authentication to Trusted Account. Enter credentials of an account that is an administrator