That's a pretty gross simplification. Around the time of the Civil War, there were more than two significant parties (including Whigs, Progressives, etc) and they were much less clearly left/right polarized in today's terms. Over the next 100+ years, there was a lot of shifting of policy priorities (from war, to slavery, to business, to civil rights, etc) followed by consolidation culminating with LBJ that left us with the two modern parties.