Although I am not a "Republican" (or a "conservative" or "right wing" etc.), I think that this statement is misguided. Much of the rhetoric of Republican politicians (I assume you are not discussing theorists) surrounding originalism as a constitutional theory (and the Republican platform in general) urges "States' rights" and restrictions on the federal government. This is antithetical to the idea of nationalism. Moreover, any political theory justifying “the state” (short of cosmopolitanism and world government) perpetuates an “us vs. them” mentality. It separates people by geographical boundaries and asserts special obligations to “fellow citizens” that do not apply to “outsiders.” So I think that your hostility towards the Republican platform is too narrow and under-inclusive.
Also, your focus on the authority of the past is somewhat misguided as well. One thing to notice about the nature of law is that all laws, absent an expression to the contrary, claim authority to bind future generations. Any theory justifying the authority of law justifies the authority of one generation to bind future generations. Notice that a law enacted by Congress in 1934 is valid today, absent an express change or amendment.