When a client says that they can't afford the dollars you're asking say for a new branding campaign or website design, what they are really saying is that it's not worth that money to them. It's not worth it to them to change their priorities and move your item to the top.
So how do you handle this? Instead of dropping your prices (I've don't it before and lived to regret it big time... most of us have) you need to take the situation in hand and bring them to the realization that they can't afford NOT to.
Your services are worth what you charge or you wouldn't be in business at all. One assumes that you've looked at what your competitors are charging and in general the cost benefit of a given product or service within a given industry.
So what makes your service worth it? That's the answer. Explain the real cost benefit to your client. If they don't change their mind... then you've done what you can. Maybe they'll find someone to do it for less, maybe not. But you at least won't have wasted your time earning less than you're worth.