The government has every right to determine whom and what is coming into the United States.
The notion of governments having rights is doubly complex.
The Federal government in the case of the US has no rights, it has duties & obligations, and powers granted by the governed specifically to carry out those duties & obligations, and only those duties & obligations included specifically in the US Constitution.
It also includes a list of specific restrictions upon what powers the government may or may not exercise and how in areas that were felt to be particularly critical to creating and maintaining a society designed for maximum individual freedom, general order & prosperity, personal responsibility, and the protection of private property rights.
In my nearly 6 decades of experiencing firsthand the changes and the impact they had at the time that many younger people here only read about in wikipedia, I've seen and continue to see more than a correlative relationship between the trend away from the restrictions on government power from the early 1900s up to current times and it's resultant explosion of government spending/debt, abuse/abridgment of civil rights, the surveillance state, and the overall general trend of decline of the US domestically, socially, and internationally in nearly every way.
Government is in some ways similar to a nuclear fission reactor-based national power grid. You only place enough fissionable material in each reaction vessel of a number of reactors to achieve critical-but-stable output to power a limited area, you don't try to place all the fissionable material in one reactor at once to avoid the costs of building multiple reactors. Well, you'd only do it once, and very, very briefly at any rate, heh!
Once government power exceeds "critical mass" and the chain reaction of growth of power cascades, an authoritarian government is the inevitable outcome. I believe there's still time to at least avert the worst scenarios, but not much time. And the longer we delay, the worse things will become and the more people that will suffer.