For us, it isn't a certain amount of money, but would depend on the circumstance and diagnosis. I would not spend thousands of dollars on chemo and radiation, for example, if the oncologist told us (with pathological backing) that the odds weren't great. I've seen too much of that to do it to my pets and I feel very strongly about quality of life vs. number of days lived.
For surgery that had good odds, I'd put it on a CC, regardless of the amount, and hope for the best. Same with any other illness that we had a reasonable chance of curing. Luckily I have some inside knowledge and several friends who are vets in various specialties; the extra info and assistance makes a difference sometimes in type of care and also in how frank they are about probable outcomes.
Basically, we go into pet ownership knowing that it's going to be ungodly expensive. They cost what they cost. They depend on us to care for them. And it's our responsibility to do that.