Sounds like the database is corrupt. Are there any other messages during the publish or when you are editing products or pages?
Before you do much messing around with the database you should make a copy of the database. You will need to do this on the server since ShopSite will check the database if you ask to do a backup within the program and it won't make a backup if the file is bad.
The file you need to backup is called shopsite_db and it will be located in your store's data directory.
If you are hosted at a ShopSite partner you should ask them for assistance with the issue. If you are not with a ShopSite partner that provides support and if you don't have annual support directly from ShopSite you should probably purchase a support incident at
http://shopsite.com/support_pricing.html to see if the database can be salvaged.