I think that "The Family" is their term for the group of Congressmen from both parties who meet for breakfast and prayer (including, last time I read of it, Hillary Clinton).
Here's another instance of leftist hypocrisy-they're always throwing "the big tent" in the faces of Republicans (Heavens how I hate that term and concept, I wish the person who came up with it would've kept their mouths shut), our "tent" is supposed to be so big that we endorse the policies and agenda of our political opponents (like Scozzofava running as a Republican, getting the money and support, then turning around and endorsing the rat when she wasn't wanted).