Although this article is a bit scary, the title is completely editorialized. Nowhere does it indicate that this is the "end of public research." The republicans are simply asking Americans to review publicly funded projects.
I think allowing the public to decide what scientific research to fund or not is a horrible idea.
Asking the general public to evaluate the contributions, impact, applicability, etc. of a research project is a pretty good way to get a lot of useful projects shot down. There's a reason we use people who know enough about the fields in question to recognize good, useful research when they see it.