I am always wary of clients that will squeeze too hard. I don't want to have to compromise on the quality of service so after I quote I don't really leave a lot of wiggle room. My guess is that if a customer is being unreasonable then they likely won't value your work in the future and that will lead to bigger problems. Sometimes you just have to walk away....

I did this recently with one of my core clients and it relived a lot of my stress.