Not sure about that distinction, because there's certainly a strain of libertarianism in Republican circles. I'll be writing soon on a similar distinction drawn by Jonathan Haidt.
Biden says there's common ground to stand on, but he has to resort to pandering platitudes or to ancient history to specify what that ground is.
As I say in the article, some of the common ground is obvious, namely our humanity or personhood, but that hasn't stopped us from fighting throughout recorded history. Obviously, those common traits (such as our autonomy) are precisely what divide us.