As I said last week - Supernatural, like most horror universes, is based on Christian mythology. The entire arc this season seems to be based on the book of Revelations, and uses the Christian version of the "devil".
(Side note - I love that Dean could not believe in ultimate evil anymore than he could believe in ultimate good. "Lucifer" is a fairy tale told in demonic "Sunday school". He's very consistent.)
But someone explain what would be significant about the number 66. I know there's a numerology reference to 666 (although is that based on Hebrew or Greek?), but sixty-six just seems out of nowhere. It's not even composed of important numbers - eleven, three, two. Okay, I'll give you three for the Trinity, but what do two and eleven mean?
(Other than the number of the tablets and the stars in Yosef's dream, but that's a Passover song.)