Physics for Future Presidents is a course offered by Richard Muller at Berkeley. The course is intended primarily for liberal arts types, but Muller opened the course up to physics majors because the subject matter is not typically covered in the required courses.
This course really is amazing: it covers the essential science to understand modern technology, especially the technology that is likely to make a big impact on our lives, and is interesting besides. Nuclear power. Spy satellites. Low earth orbits. Moore's Law.
The objective of the course is understanding, not computation. An entirely reasonable goal. As Muller says, if you really need to calculate something physical, you hire a physicist (or an engineer). However, you need to be able to understand the science well enough to make a good judgment about what you are given, and what to do with it. Something along these lines would be much more effective than forcing all college students to take lab science, because this class effectively focuses on the big picture. Learning how to titrate in University Chemistry I does not necessarily make for scientific insight or good judgment. Learning how to compute a surface integral for Gauss' Law is really no better for that purpose (albeit fun).
That being said, I don't know how well this course would work on the general student population at say, Northern Arizona University (my alma mater). Jokes about liberal arts majors aside, anyone who gets into Berkeley is pretty damn smart. Students at a state college are much closer to the population mean in intellectual ability, so this course may be too hard for them as is. However, I think there is something to this. The science courses offered at most universities really are more like vocational training for scientists than the building blocks of a liberal education. The unelected elites that Charles Murray talks about really do need to understand science, but good judgment is more important than the calculus.
If you ever wanted to know more about science, but hated the classes, or couldn't hack the math, buy the popular version of the book, or watch the lectures on YouTube. It would be better if more people understood science in this fashion.