We just published the Community in our Sandbox, and we can get to the correct Home page using the "Log in to Community as User" link on a Community User record. However, when I log in to the published Portal as that user at full-xxxxxxxxx.xxxx.force.com/support, all I get is the Under Construction page after submitting my credentials. I am assuming I am missing something basic, because I cannot find anything where anyone asks a similar question unless they are using a VF home page.
