They absolutely desire this, but their implementation is going to be difficult. Certainly we are seeing fascists test their ideas and what works right now, and I worry for what comes well beyond the Trump Administration. To be fair, Trump's Administration is really an extension of the Bush Administration's policies. The destruction of public education for example didn't begin with Trump, nor Bush, for that matter. But began with Reagan. The process has been long and slow over the course of 40-50 years. First, make higher education significantly more difficult to obtain. Then increase tax dollars going to private institutions and reduce tax dollars going to public institutions (School Voucher Program under W), to now just absolute flat out destruction of the federal Department of Education (Trump era).
ICE didn't exist until George W Bush (Homeland Security Act of 2002), and much of its powers stem from this act.
In short, much of the power that Donald Trump derives today was directly adopted by the Republican Party after 9/11. This is why it's critical to follow these laws.
With the talk of denaturalization, and potentially modifications/reinterpretation of the 14th Amendment, this only furthers these aims that were started over 2 decades ago under the guise of Republican leadership. In fact, the Republican Party has basically only accomplished two things in the last 25 years: A significant restriction of rights for everyday Americans, and massive fucking tax cuts for the wealthy.
If the 14th Amendment goes, and it looks like it's in the crosshairs, that is a significant step up that will inevitably allow Republican leadership to define citizenship however they wish to do so. And that should be scary as fuck.
In short, stop voting Republicans for any office, at any level of government.