This is happening in the login phase - I think this error indicates that you're not actually talking to Tableau Server.
Check the Tableau Server server name and the port number in the Desktop login dialog again. I dunno, make sure you didn't type the SharePoint server name by mistake or something?
I might be wrong - it's weird that you'd have problems logging in only for this workbook/datasource. But before the next publish dialog shows up, you haven't actually published the current document. Try this experiment: Open the workbook, then select Server -> Login instead of Server -> Publish workbook. Can you login successfully? If so, then try to publish after logging in - do you get the same error?
This was definitely in the ballpark of the issue...weird.
I was using the correct login, and actually was able to publish another workbook using another SharePoint oData connection, immediately after building this first workbook, without any issue.
When I sat down this morning, reconnected to VPN, and attempted to login again (was going to play around with your suggestions above), it magically worked. Not sure what got tangled up here, but it was definitely login related as you suggested. I'll keep that in mind if I ever hit the same issue again.