Instead of
http://www.example.com/index.html you will need to enter
http://www.example.com/backupdirectory/index.html.
The problem is going to be the links between pages in the backup site either pointing to backup URLs and thus needing to be changed when the site goes live or links going from a backup site's pages to a current site's pages.
More work for you. Hope you included the extra time in your proposal.
Regards,
Rod