The bike shop is busy in June. If you bring your bike in for a tune up, it will cost $39 and take a week.
What if someone says, "I have a bike trip coming up in three days, can you do it by then?"
At most bike shops, the answer is a shrug, followed by, "I'm sorry, we're swamped."
The problem with telling people to go away is that they go away. And the problem with treating all customers the same is that customers aren't the same. They're different and they demand to be treated (and are often willing to pay) differently.
So, why not smile and say, "Oh, wow, that's a rush. We can do it, but it's expensive. It'll cost you $90. I know that's a lot, but there you go."
Outcome: Maybe they'll still leave. But maybe they'll happily pay you for the privilege of doing business with you. Why should this be your choice, not theirs?
If you do tax accounting for mid-size businesses, why not offer a special last-minute service? A service in which you process shoeboxes filled with unsorted papers? A service that costs less but happens during your slow season?
There are two really good reasons to turn down special requests:
1. because you're marketing yourself as extremely busy and perfectly willing to turn down good work.
2. because you want to market yourself as someone who is a rigid artist, a stick in the mud or a crotchety perfectionist. This works great for pizza places.