I followed the steps from Egit user guide, but I get an error message with auth fail.
What I do:
I have copied the public key from Window >
Old question, but for future reference:
Make sure you did setup a push remote. It worked for me when I got both the Cannot get remote repository refs-problems ("... Passphrase for..." and "Auth fail" in the "Push..." dialog).
Provided that you already:
Setup your SSH keys with Github (Window > Preferences > General > Network Connections > SSH2)
Setup your local repository (you can follow this guide for that)
Created a Github repository (same guide)
... here's how you do it: