I have a repo that is a bare clone of a github repo:
git clone --bare firstname.lastname@example.org:PabloSerbo/maiden.git
git fetch origin
clone the bare repo yourself. This will have origin pointing to that. Now add the github repo as 'github' remote. You can now fetch the branches and tags from github and in turn push them to origin.
git fetch github git push origin github/yourbranchname:yourbranchname
Hope this helps.