Absolutely. The Democratic party has moved much farther left into what I would define as a Nationalism and Socialism, but not of the NAZI brand -- which was never "right wing."
And the Republicans have also adopted a more Nationalistic stance, with more Socialism, liberally spiced with religion (many consider this part "right wing") -- wanting to break that Church and State wall down.
In layman's terms, and generally speaking, the Democrats want your economic freedoms curtailed, while you keep most of your personal freedoms (Abortion, free speech etc.). The Republicans will allow you slightly more economic freedoms, but wish to curtail your personal freedoms.
It's an "American Dichotomy."