Are skunks quick to spray or do they really have to get annoyed and riled up before they release their juice?
Mainly, it’s a “I’ve shown you my ass, you’re in range, and you’re still advancing” thing.
I don’t know the answer off the top of my head, but there is an obvious empirical solution. Get a skunk and gradually provoke it more and more until it sprays. The answer is therefore a little less than that.
I dunno, some skunks are twitchy; yanno?
Honestly my anecdotal experience is that at least Striped Skunks in my area ( both suburban and in nearby parkland with at least some human exposure ), is that they are remarkably tolerant in a very arrogant sort of way.
I’ve been sitting on the ground in an oak woodland and had a small skunk forage in the leaf litter five feet from my foot. When I twitched, it gave me a quick warning glare, but didn’t fire and quickly went back to foraging. I’ve had one get invade a cooler with a broken lock at a campsite and though we were unable to shift it out, it didn’t bother spraying to keep us away - it just gave us a “look” and went back to eating our cheese. etc.
When you have those sort of defenses ( which I’m sure they quickly learn will make any mammal retreat quickly ), I imagine you can afford to be semi-tolerant of most anything. Great Horned Owls excepted ;).
And some are peppy. Of course any experimentor worth his salt would do this with multiple skunks, with some blind-folded.
When I was a kid, I had a dog that got skunked not once, not twice, but THREE times in one summer. I mean how STUPID was that dog. I mean I know you’re a dog and you’re guarding your property but c’mon, it’s a black and white animal that got you twice already. 
That said, after spraying it takes a skunk about 10 days for a skunk to replenish it’s “Skunk supply” once it fully sprays, so they are not going to go around spraying unless they have to
We used to have a family of skunks visit our back porch to eat any cat food that was left over, and we’d watch them through the glass door. They don’t have great eyesight, but if we made a bit of a noise as we opened the door they would scamper off. I never did try to sneak up on one, but they seemed to move away quickly if warned. I haven’t seen them in a few years, and even if they were still around I wouldn’t volunteer to gather any empirical data for you. We did smell them every couple weeks or so, and figured the local coyotes had a chance encounter with the skunk.
Skunks know that they are not to be fucked with. I don’t recall ever having one raise its tail to me. I also know better than to antagonize it. It gets pretty hot here during the summer, and I’ve actually had a skunk walk into my house through the open back door and go all the way into the kitchen. Now this is freaking me out. I build a little corridor through my house out of boxes and then go outside with a water sprayer, shoot at it through the window, and gently coax it out of the house. Phew, no pew!
Well, you know dogs. You give them a bath and they go roll around in the garbage. I think they like to stink.
I notice there’s no “Need Answer Fast” in the header…
When Mythbusters was trying to test various skunk odor removal recipes, they couldn’t get their test skunk mad enough to spray at all.
I’ve been withing a couple feet of skunks here in the park several times. My view is that they don’t want to waste anything. They go about their business. If the threat is gradual like a person walking towards them, they will stand up and wiggle their tail a bit. You see a white flag so to speak. If you keep getting closer, they could let lose. I have run buy within two feet with no problem. That has happened when running in the dark where I did not see them. If the threat to them is positive like an approaching dog, they are going to wait for close range and then shoot. They will shoot every dog, even a friendly one.
It take time to “reload” their smell sack, perhaps a few days. There’s no “fuel gauge”. Skunks do not know how much is left. Therefore, they’re a bit cautious about spraying because they don’t know if they might need it again in the near future.
This vital tidbit brought to you by the department of redundancy department.
When I was in college, there were quite a few skunks that would hang around the dining hall and many of the student, myself included, would hand feed them. They got very used to people and never sprayed anyone to my knowledge. About the most I ever saw was one raise his/her tail if someone suddenly made a move towards them instead of approaching slowly or waiting for the skunk to come to them. Even then, they always scampered off rather than spraying because they knew they had a good thing going and didn’t want to scare away their free food supply. To get those skunks to spray, you probably would have had to physically grab it.
Really, there is no answer to the OP’s question because the amount of provocation will vary widely from skunk to skunk. I suspect the campus skunks needed a lot of provocation to spray. Meanwhile, if some other skunk had rocks thrown at it from a hundred feet away by a group of kids all wearing red hats, and you happen to go jogging by the next week 20 feet away in a similar red hat, don’t be surprised if you get nailed.
I have run into skunks many times when hiking with my dogs and my experience is consistent with the other posters. Skunks are very confident (or arrogant) and will generally go about their business if left alone. If they feel threatened, they will do an elaborate and extended warning “dance” that includes puffing up their fur, much ground stomping, and furious tail twitching before they resort to spraying.
Much to my chagrin, despite all the advanced warning the skunks give, the dogs still seem to get sprayed about once a year. They have no one to blame but themselves.
My paternal grandfather once rescued a skunk that got caught inside a roll of barbed wire - it didn’t spray.
OTOH, my maternal grandmother once famously chased a burglar out of her house with a broom, and he jumped over the backyard fence to escape - landing near a skunk, which sprayed him (it surely was not his day). The cops had no trouble finding him … my mom was supposed to be writing a paper that night, and in the excitement, she failed to do it & tried to explain to the teacher why … he didn’t believe her until she was able to produce a newspaper account. 
They do give you warnings beforehand, either twitching their tail and turning their back end toward you, or occasionally, skunks will do a handstand before spraying, to let you know they mean business. I got the handstand once while driving through a pasture at night. The skunk got caught in my headlights and immediately went into handstand mode.
I’ve had skunks visit my campsite over the years; IME, the best thing to do is just let them go about their business. As long as there isn’t any food around, they’ll move along without any trouble. We had one snooping around under our picnic table…my girlfriend was ready to freak out, but I calmed her down before she could spook it. It waddled away to visit the next campsite, where the campers were strung a little higher…there were screams and people running to the four winds, which we found highly amusing.