If you include your username and the repo name we can reasonably help you, at the moment we have no reason to think the repo does actually exist.
Additionally, if the repo is private and you don't have access to it, github returns "Does not exist" to avoid disclosing the existance of private repos.
EDIT: If you're not able to clone it because it's saying it doesn't exist and it's private, it's because you're not sending authentication. Ensure that your public key is added to your keyring, or use HTTP basic auth for the time being.