Current discussion thread: http://devnet.jetbrains.com/message/5519081#5519081
Bug Report: http://youtrack.jetbrains.com/issue/TW-37148
Error: Cannot prompt for input in non-interactive mode.
One thing to note is that the credentials prompt is triggering on each package download instead of at the beginning. I think this may be a bug in the way Team City is calling NuGet, but I'm not sure.
I have the "NuGet Feed Credentials" build feature configured, basic auth configured, and I've run the feed in Firefox and got the list of packages to show up on the agent machine (with credentials required).
My build log: https://gist.github.com/tonyeung/517597ca2312dad85f62