It was on Tony Snow's Fox news show, not the Senate Floor. His actual words were "There are white niggers." He was forced to apologize.
http://www.why-war.com/encyclopedia/people/Robert_Byrd/ Byrd was a member of the Ku Klux Klan for a period of time in the early 1940s. In a letter he wrote in 1946, he said, "The Klan is needed today as never before and I am anxious to see its rebirth here in West Virginia." However, by the time he ran for Congress in 1952, he announced, "After about a year, I became disinterested, quit paying my dues, and dropped my membership in the organization. During the nine years that have followed, I have never been interested in the Klan."
2001 racial remark controversy
On March 4, 2001, an interview with Fox News Sunday host Tony Snow was aired. In the interview Byrd was asked about race relations: "They are much, much better than they've ever been in my lifetime," Byrd said. "I think we talk about race too much. I think those problems are largely behind us... I just think we talk so much about it that we help to create somewhat of an illusion. I think we try to have good will. My old mom told me, 'Robert, you can't go to heaven if you hate anybody.' We practice that." Then Byrd warned: "There are white niggers. I've seen a lot of white niggers in my time; I'm going to use that word.
"We just need to work together to make our country a better country, and I'd just as soon quit talking about it so much."
Byrd's office later issued an apology.
"I apologize for the characterization I used on this program. The phrase dates back to my boyhood and has no place in today's society. As for my language, I had no intention of casting aspersions on anyone of another race."
American conservatives have pointed to Byrd's comments as evidence of a double standard in the treatment of Democratic and Republican political figures in regards to controversial statements about race (see Trent Lott, Rush Limbaugh).