I don't know why @aparente001’s answer was downvoted. I teach mathematics at a liberal arts college, and when we hire, a detailed research statement is not very important, but a research area that has the possibility of involving students is a plus, and we’d like to hear about how you might do that. But chances are good that no one in the (very small, teaching-focused) department will be well-informed about your specific area to be interested in great detail.
What I look at first is the cover letter. If it’s nothing more than a summary of your CV, and/or mostly about research, my interest is diminished. If it’s not well-written (good communication skills matter, even in the math department) I’m worried. But if it elaborates sincerely and believably on “Your position interests me because I want to teach at a liberal arts college. Here’s why.” If it shows you did your homework and know some particular things about my university that attract you (and I don’t mean generic praise for “our excellent reputation” and “strong department”) I’m more interested.
We (I don’t know about all liberal arts colleges, but I might speak for many) want great teachers who will remain professionally active and engaged in their discipline, but that can be interpreted broadly and doesn’t have to include a fancy research program. We also like colleagues who are interested in other disciplines. Maybe you’re a world-class analyst, but we’d rather hear you tell us about the time you helped an art student study perspective for her thesis than tell us about your improved bound for some well-known (to analysts in your area) asymptotic formula, not that there’s anything wrong with that. We’d rather read your thoughtful blog on teaching or frequent, patient and carefully written answers on math.stackexchange.com, too.
Related to your question is the issue of recommendation letters. All too often we get letters for new R1 Ph.D.'s that go on and on about research and assume we know all the best young recent Ph.D.s from that school (“Janet’s research is comparable to ”) and then barely mention teaching (“She gave a seminar talk that was very good,” or “She spends a lot of time with students during office hours.”) This, even though we ask for letters that specifically address teaching excellence or potential. Tell your letter-writers that you want them to address your creativity, your ability to explain, your cross-disciplinary interests, and so on. Perhaps even choose teachers you think you did great homework or exams with, or ones you T.A.’d for. Even a letter from a LAC faculty member who finished a few years before you, knew you well in graduate school, and has kept in touch with you.
Honestly, I find it incredible (not in a good way) that so many R1 senior faculty think the research-focused letters they write will be helpful at places like LACs. It’s more understandable that applicants don’t know what we want, but asking, like you’re doing here, is a great idea.
