I have a similar problem, running 4.0.1210.0 and tried to modify a form when I recived the same error message.
Invalid provider name "Default" for SitefinityMembershipProvider specified in web.config file. The name should match one of the providers configured in Sitefinity's Security.config configuration.
The site was inaccessible from then on, so I cannot get to the backend admin functions (or any area of the CMS).
Any attempt to access the site or login to Sitefinity returns this error:
Server Error in '/' Application.
Cannot find the object "sf_contact" because it does not exist or you do not have permissions.
There is no Default Provider defined in the SecurityConfig file. Will adding one correct this issue?