One source of difficulty with YEC (Young earth creationism) is the fact that, even without evolution, there is a problem with astronomy. I haven't heard anyone arguing that we should teach alternative doctrines of astronomy in public schools, but if "the heavens and the earth" were created in six literal days, and the age of not only the earth but the universe can be counted up through the genealogies, you get not just an earth but a universe that is approximately 6000 years old. What this means is that anything that is further out in space than 6000 years should not be visible, because the light from those stars would have to travel more than 6000 light years to get here, which would break the intergalactic speed limit. Nevertheless, we do see stars millions of light years away, according to astronomy.
I am linking to a site from Answers in Creation, which raises this issue for YEC.
Is modern astronomy an attack on the God of the Bible? Why are conservative Christians upset by evolution, but never upset by simple astronomy? Why do Christians sometimes think the Devil made Darwin do it, but they never worry about whether the Devil made the astronomers do it. Yet astronomy strikes me as being as big a problem for lead-footed literalism as evolution.