I am writing this as a former left wing radical and card-carrying member of the Labour Party. In my opinion the whole "YouCut" episode is nothing to do with the public understanding of science and all about the toxicity of modern American politics.
It's a widely acknoweldged fact that Americans have a deep distrust of intellectuals. This is something that the Republicans have never been shy of exploiting and even Democrats have had to acknowledge. It's no accident that one of America's smartest presidents ever (William Jefferson Clinton: Georgetown, Oxford, and Yale; Rhodes Scholar, etc.) spent most of his presidency honing his best Jed Clampett impression. Sad to say, the current president may be brought low because he's smart, well-educated, and not afraid to show it.
Of course, I'm not dewy-eyed enough to believe that political factors play no role in the award of large grants, especially and the mega-grant level, but NSF is scrupulous in its employment of peer review, to an extent not matched by all Federal agencies. The idea of all that potential pork being handed out on the say-so of a bunch of pointy-headed intellectuals must drive Members of Congress batty.
Of course, the problem with taking a "negative" stance is that while it's much more fun, it doesn't really take you anywhere. So that's my challenge to the "YouCut" people. Rather than the public telling us what should be cut, why not have them tell us what should be funded. Pick your favorite proposals and then let's publish them and see what everyone thinks. No? Well that's not surprising. Because that's not the debate that you're interested in having, is it?