Heya, I am by no means discouraging anyone from answering your question, but I think you'll like this thread where /u/x--BANKS--x, /u/Samuel_Gompers and others answer and discuss that exact LBJ quote:

https://www.reddit.com/r/AskHistorians/comments/2088gl/president_lbj_ill_have_those_ns_voting_democratic/