The comment was made while he was talking to two Governors on Air Force One. It was documented in Ronald Kessler’s 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:
“These Negroes, they’re getting pretty uppity these days and that’s a problem for us since they’ve got something now they never had before, the political pull to back up their uppityness. Now we’ve got to do something about this, we’ve got to give them a little something, just enough to quiet them down, not enough to make a difference. For if we don’t move at all, then their allies will line up against us and there’ll be no way of stopping them, we’ll lose the filibuster and there’ll be no way of putting a brake on all sorts of wild legislation. It’ll be Reconstruction all over again.”