From the Snopes link: “There’s no question that Lyndon Johnson, despite championing the landmark Civil Rights Act of 1964 and signing it into law, was also a sometime racist and notorious vulgarian who rarely shied away from using the N-word in private. For example, he reportedly referred to the Civil Rights Act of 1957 as the “ni**er bill” in more than one private phone conversation with Senate colleagues. And he reportedly said upon appointing African-American judge Thurgood Marshall to the Supreme Court, “Son, when I appoint a ni**er to the court, I want everyone to know he’s a ni**er.”
According to historian Doris Kearns Goodwin, he also uttered this cynical-sounding statement, which sometimes circulates in tandem with the “voting Democratic” remark:
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.”