I am using Visual Studio 2013 to manage a .sqlproj file containing our database schema. The schema has been deployed successfully dozens of times.
When attempting to pub
This happens when there exists a stored procedure (or view or constraint or other object) in the target database, that isn't included in your sqlproj, that references a table that would be altered by deploying your sqlproj. SSDT apparently can't determine whether the change is safe unless the referring thing is included in your sqlproj, and then it errs on the safe side by blocking the deployment.
Disabling the "Block incremental deployment if data loss might occur" option only relaxes the data-loss checks. There isn't a "Block incremental deployment if run-time errors might occur" option.
You have three options:
add whatever stored procedures, views, or whatever from the target database to your sqlproj
uncheck the "Verify Deployment" option in the ssdt publish options (this is dangerous unless you're aware of the other referring sprocs and know that they aren't going to break)
if you're certain that everything that should exist in the target database is contained in your sqlproj, you can enabled the "Drop objects in target but not in source" option