This reminds me some of the movement that led to Heller redefining the 2nd Amendment to protect an individual right to bear arms. A lot more ground work had been laid there but there are similar originalism arguments for the 14th to overturn 150 years of precedent and an earlier Supreme Court case. The thing about originalism is you often have your pick of original interpretations so it can be a vehicle for activisim. Here they'll focus on "subject to the jurisdiction thereof" to exclude undocumented immigrants. It's not a totally far fetched argument, though it goes against mainstream legal thinking. That the second amendment protected an individual right also went against mainstream legal scholarship and we know how that turned out. Both the majority and dissent in Heller relied on originalist arguments.
There's also a lot of dumbing down in the media of what Trump would actually do with an EO. It wouldn't change the 14th amendment. An EO would setup a legal challenge that could eventually lead to, depending on your views a reinterpretation or clarification of the 14th amendment. It's just like states passing laws to test Roe. There may be other issues with executive power and if an EO is contrary to a statute providing for birthright citizenship but those are different issues than this idea of changing the constitution by EO. Trump, or at least his handlers, know that's not possible.
The policy of birthright citizenship is also a lot more complicated. Birth tourism is clearly problematic but the certainty birthright provides is important. Eliminating birthright citizenship would drastically expand the number of people who, like the dreamers, are American in every day but under the law. That's a big problem.