Twitter's privacy policy doesn't actually require a warrant to give up your "private" info (including your protected tweets).
Law and Harm: We may preserve or disclose your information if we believe that it is reasonably necessary to comply with a law, regulation or legal request; to protect the safety of any person; to address fraud, security or technical issues; or to protect Twitter's rights or property.
I doubt Twitter gives them everything since it's a difficult engineering problem to handle that much data. But I could easily believe the FBI has a list of terms or phrases that Twitter self-monitors for.
Law and Harm: We may preserve or disclose your information if we believe that it is reasonably necessary to comply with a law, regulation or legal request; to protect the safety of any person; to address fraud, security or technical issues; or to protect Twitter's rights or property.
https://twitter.com/privacy