Nginx – Login with Google for nginx

I have a nginx server serving protected resources. The last thing I want to do is manage password reset requests, so I was looking at Login with Google.

They have examples for PHP, Java, JavaScript etc., but not for Apache or nginx. How can I configure nginx to swap out basic authentication with the Login with Google functionality?

Some proxied systems behind depend on the %REMOTE_USER% variable, so I need that one preserved.
Help is appreciated.

Update
To clarify: I have a set of services (a tomcat, a node.js, a couchdb, a vert.x, some python) that sit behind the web server, that might or might not authorize a user to interact with them. They all have in common, that they can receive identity information from the web tier.

So what I do in the web tier: specify – "authenticated users only" (which is a authorization setting, I "reuse" to trigger the authentication mechanism).

Once the user is authenticated, that identity information is passed on. For an example with basic authentication and CouchDB, check this blog entry. I can do the same in nginx, but the task here is to burden someone else with keeping a password secret using identities established with an outside provider.