The comment was made while he was talking to two Governors on Air Force One. It was documented in Ronald Kesslerās book,
Inside the White House..
From the Huffington Post:
The Democratic Party's Two-Facedness of Race Relations | HuffPost
Here's another quote from LBJ:
āThese Negroes, theyāre getting pretty uppity these days and thatās a problem for us since theyāve got something now they never had before, the political pull to back up their uppityness. Now weāve got to do something about this, weāve got to give them a little something, just enough to quiet them down, not enough to make a difference. For if we donāt move at all, then their allies will line up against us and thereāll be no way of stopping them, weāll lose the filibuster and thereāll be no way of putting a brake on all sorts of wild legislation. Itāll be Reconstruction all over again.ā