The job market is (generally speaking) less about the school you went to and more about who you studied under in your subfield, and additionally, how well-connected your department is in terms of job placement. If you want to grow up to become a scholar of Queer Theory in Shakespeare, you need to go find the person who does that, study with them, and go forward, ideally with your POI starting to put out feelers to place you in a job long before you finish your dissertation. The caveat to that, of course, is that a lot of "the greats" are at the Ivies, and folks at the Ivies are extremely well-connected. Are they more connected than folks at UCLA or Michigan? That probably depends a lot on your subfield, area of study, and other factors. So the name might not do much, but the name comes with connections that might. Make sense?
For what it's worth, fit on the job market is related to so many factors. At my university, we've actually seen a lot of people with amazing Ivy educations not make it to the last round of searches because their background just doesn't match the program of studies we offer (in that it's much more classical than what a lot of our students take). These are amazing scholars who go on to be highly sought after elsewhere, but just aren't the right fit for what we offer.