For you who, like me, already did setup you ssh-keys but still get the errors:
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:
- Go to the Git Repositories view (Window > Show View > Other > Git Repositories)
- Expand your Repository and right click Remotes --> "Create Remote"
- "Remote Name": origin, "Configure push": checked --> click "OK"
- Click the "Change..." button
- Paste your git URI and select protocol ssh --> click "Finish"
- Now, click "Save and Push" and NOW you should get a password prompt --> enter the public key passphrase here (provided that you DID (and you should) setup a passphrase to your public key) --> click "OK"
- Now you should get a confirmation window saying "Pushed to YourRepository - origin" --> click "OK"
- Push to upstream, but this time use "Configured remote repository" as your Destination Git repository
- Go get yourself a well earned cup of coffee!