In 1940, FDR's conservative Vice President (John Garner of Texas) was so fed up with the liberal policies of the New Deal, he ran against FDR for the Democratic nomination. He failed.
A few years later, in 1948, a large bloc of Southern conservative Democrats broke away from the Democratic Party and formed the States Rights Democratic Party.
States Rights! A core right wing principle to this day.
Platform of the States Rights Democratic Party
"States rights" was the term used by the Democratic conservatives to preserve racial segregation, and is still used today to oppose federal civil rights legislation. The term was used by old time Democrats in place of naked racist rhetoric to woo Republicans to support the Southern Democratic minority in Congress. They couched their language in terms of preserving the Constitution when their true aim was to preserve segregation and deny voting rights to blacks.