I think a well-known rule of writing applies here: Show, don't tell, in the same way it applies to parenting. If you want to help change your students' feelings, you need to show them your love for the liberal arts.
One thing you can do is pepper your courses with relevant analogies, stories and quotes from literature, history and philosophy. For instance, a discussion of Zeno's paradoxes and maybe some things about the ancient Greeks when discussing limits in calculus. Or some historical context for Newton. I don't have any good contextual literature examples at the tip of my typing appendages (maybe something in Lewis Carroll?), but it's easy to preface new topics with semi-relevant quotes such as
The sense of danger must not disappear:
The way is certainly both short and steep,
However gradual it looks from here;
Look if you like, but you will have to leap.
-- W.H. Auden
Even just displaying some of your favorite pieces of literature in your office can be good. This has led to a few literature discussions with students for me, and discussing literature with students who are interested in front of students who aren't can help convince the latter literature is interesting.
Of course, you won't be able to suddenly convince everyone that they need to run out and read Herodotus in the original Greek to figure out what history class they should take next semester, but you can make some impact for some students this way.
Incidentally, I personally hated having to take the GenEd requirements when I was in college, because there were loads of Math/Science courses I wanted to take. But then when I went to grad school, I wasn't in such a rush, and I read a lot of classics. So many of the students may not be at the right stage of life to appreciate everything. (Also being forced to do something generally makes it harder to enjoy it---in science or liberal arts.)