In what situation would you lower your rate..

I recently got an email from a potential client. They have the design already done in a PSD and half the HTML/CSS converted already for me, they just need me to implement it in the Rails framework and do the back-end work. I was thrilled to hear this in the email, but after sitting down talking to them for a half an hour over Skype, I found out that their budget is a little under what I came up with after going through all the requirements. I told them I would get back to them with an exact project rate as they requested. If I lowered my rate to $50/hour instead of $75/hour (the lowest I will take), I could make it on time and on budget, but on the other hand, I have bills to pay, especially in my current situation.

What would r/freelance do?