The Democrat Party of our grandfathers began desolving with FDR and Henry Wallace, his Vice President. Wallace was replaced as Vice President by FDR with Harry Truman in 1944 elections. Supportedly over differences in personal policy.
Wallace became the presidential candidate of the Progressive Party and was endorsed by the American Communist Party in the 1948 elections. This was also the time of the formation of the Dixiecrat Democrat Party. Remember Strom Thurmond and the comment of Trent Lott? Anyway the Democrats of 1948 were split into 3 factions as they did in 1860. After Truman won, the Democrats in the south found themselves more and more on the opposite side of the Democrat Party policy.
To make a long story short, the platform of the Progressive Party in 1948 is what the modern Democrat Party now supports.