I have been trying to research this question myself, but haven't been totally successful.
Does a federal officer have the right to ask me for ID just because I am on public land? For instance, if I am camping on BLM land or Forest Fervice land, and am abiding by all the regulations and there is no reason to suspect any illegal activity, can the BLM officer demand my ID just because he is a federal officer? If so, where does the US Constitution, or US Federal Statute allow this?

I am aware of Terry vs. Ohio, Hiibel vs. Nevada, and the recent case where passengers on a city bus were asked for ID when going through a federal building in Denver. None of these cases really applies to my question.