Can't SSH into my Mac from Linux
If you're getting timeouts, that has nothing to do with your authentication mechanism - whether password, or key based.

The timeout means either you can't connect to the Mac at all, or it's not accepting traffic on port 22 (the SSH port)

Some things to check - 


Have you checked your firewall is off on the mac? System Preferences -> Security -> Firewall
Can you ping the Mac from the Linux desktop? A simple ping to the Mac will verify that they're on the same network and can communicate.


Fix your network issue before you try to fix your authentication.