They ask for a discount
Them "That's a bit more than we were hoping to spend."
Do not fill the silence. Do not immediately offer a lower number. What follows is the only sentence you need, and the reason it works is that it doesn't argue.
You "Totally understand. That's the price for the scope we talked about. If the budget is fixed at a lower number, tell me what it is and I'll tell you what fits inside it."
You have not defended the price and you have not dropped it. You've moved the conversation from cost to scope, which is the only place it can be solved without you losing money.
Roughly half the time, they find the budget. The other half you build a smaller version at your actual rate. Both outcomes are fine. Discounting is the only outcome that isn't.