George Wallace was a Republican right? And Klansman Byrd, he is a -- never mind.
There were a few southern republicans also supporting the Civil rights filibuster. But, clearly, it was a regional fight, not a party confrontation. It was, in fact the Republican leader who mustered the final votes to overcome the filibuster.
http://www.senate.gov/artandhistory/history/minute/Civil_Rights_Filibuster_Ended.htm