No. Everything that makes a website great should be the complete and basic package. design,responsive,easy to use should be by default the characteristics of the website. Your not going to build them a crappy website because they aren’t paying you extra are you?
Every website needs to be responsive today and we, as designers, shouldn’t even consider delivering a non-responsive website. If you are charging by hour, make a simpler version of the website if the client won’t pay your final price, but always responsive. I prefer to charge by project. Our job is to show the clients why they need a responsive (and future proof) website today. By the end of this year, the number of mobile-connected devices will exceed the number of people on earth.