Can I share an entire Git project via Gist?

I'm writing a tutorial for users of our API, and want to incorporate code snippets and complete files for example purposes. I can expose the entire directory structure as a git, for people to download; no problem. But I'd like to embed specific code on relevant pages in the way that I can via a gist.

I do that by copying each file into gist, pressing "embed", and copying the resulting link into my tutorial page.

However, it seems wasteful to have a git repo all set up with the full files, then have to duplicate it for each file. Is there a better way to do this?

(Alternatively, if there's a way to embed a reference to a specific file from a git, I could do that too--the use case here is to say, "here's the full sample file" so I'd be fine pulling it that way.)

Thanks.