This is an easy one. Your program’s ranking certainly can have an effect, but it doesn’t necessarily spell INSTANT JOB. It also doesn’t necessarily spell INSTANT REJECT.
It all depends on the post-PhD job you’re applying for. The more closely and tangibly your skillsets and experience are a fit for the job you’re applying for, the less anything else matters, including where you got your degree.
If you have great evidence of experience doing the kinds of problem solving, management, analyses or data processing that are similar to what people do in the jobs you want, you could come from a program on the moon and it won’t really matter.
Naturally, society is at least somewhat snobbish, so biases and favoritism do happen. We can look at the number of faculty who hail from Ivy Leagues and see that academia is just as guilty of using rankings and prestige factors as any other employer, so we won’t pretend that it doesn’t matter.
But the bottom line is that in all but a few particular types of jobs where your title and pedigree are visible and attractive to an employer’s clients, what matters more is what you can do for the employer.
(This is, of course, assuming you’re not in a position to use your network or personal influence to bias employers. In that case, university ranking is a reflection of your personal influence more than anything else.)
In the end, program ranking is a proxy – and often a poor one – of the caliber of potential employee that you are. It’s used during candidate evaluation given a lack of other ways to know who you are and what you’re capable of.
Give them something better.
“Give the employer a reason to hire you that you control. Otherwise they will default to things outside your control, like program ranking, prestige markers or appearance, where they will have an unfair weight on your application.” – Free the PhD
Ask me more career questions!
Ivy League Bias in Faculty hiring: Academia’s Dirty Secret
Adapted from my Quora response.