Unless someone is already requesting the least expensive material we offer, the answer is always "yes, but..." Even then it's "yes, but you have to order 100."
CanuckSigns is correct, the type of customer that wants to nickel and dime you to death is, in the end, unlikely to order from you anyway. If they're hung up on the price of the job instead of the other details, you probably don't want them as a customer anyway. That's a huge red flag.
We have plenty of customers who play the game as it was taught to them either culturally or through work experiences. Some people just need to feel like they struck a bargain or good deal in order to justify what they consider doing their due diligence.
That's why we try to quickly perceive what kind of client it is then apply a tiered approach whenever possible.
In a related but different scenario, we're working right now on a perfect example of how to handle a customer who in this case saw something he liked somewhere but had no idea how much the raw materials cost. He isn't pressuring us to lower our price or wrestle a better deal from us, he just didn't know.
He sent us a nice, scaled schematic of an interior set of three 20"x 72" 1/2" thick frosted acrylic signs with painted 3/4" thick first surface mounted letters and logo icon with MBS style standoffs. A 4'x8' sheet of the background material alone in that thickness is about $800 with shipping. You can only get two of three signs out of one sheet, so we'd be stuck with over half a sheet of drop off and the end cuts. After getting a quote from Gemini, the letters and logo retail out at $1,200 for all three.
Before wasting much time and even sending him the first quote on exactly what he asked for, I preemptively asked if he had any idea how much these materials thicknesses cost and if he'd be open to other options. He was unaware and was very much open to alternatives. Just by offering that information, we've gained his trust and he knows we're looking out as much for his best interests as we are selling him something that is clearly overkill. Just by switching to 3/8" clear with frosted crystal vinyl applied to the face and using 1/2" thick letters, the cost dropped dramatically. We sent him an estimate with several different options ranging from his original idea down to 1/4" clear with frosted crystal vinyl and 1/2" thick letters and logo.