If by open contact you mean "face to face", it has already happened to some. You just have to be special enough to deserve it, I think.
As for the entire public, well. Like I said above, I am no psychic... but I would guess, perhaps in the next twenty years we will start to see some action, or some amazing piece of film will come forward.
No reptilian is going to walk infront of the white house and make a speech... that would most certainly result in complete termination, and if they managed to get away, they would be the most wanted fugitive in the reptilian universe.