It is also absolutely within President Trump's executive authority......
That's it.
And it clearly is detrimental to admit any more when those who are here have cheated, there is a decade-long+ delay in deporting people through "due process" as a result of deliberate obstruction and persons both within and outside the government have deliberately frustrated enforcement of existing law in active conjunction with the immigrants that are here.
......Trump needs to put up or shut up. Yes, arresting and deporting a few hundred here or there is better than zero but there are ten million illegal aliens here from the last four years that were unlawfully paroled by Biden and another ten million, roughly, who have come in before. Combine this with enforcement of 8 USC 1324 for anyone harboring or employing illegals and the problem will be solved.
The way you get industry and everyone else to demand they all leave is to prohibit any more, legal or otherwise, from entering until they do. The Chamber of Commerce with their H1-b, H2-a and J-1s along with all the legal migrant visa-bearing labor can either demand they all leave or they have no more of their imported labor until they do.
Yes, its a nuclear option -- and we're well past the point where the nukes should have already been used.