I would go as far as asking, as I just happen to have coincidentally done this past Monday, how and why the potential client came up with that budget.
After getting the answer or not, I'd politely decline and offer no recommendation or referral as I do not know a single professional that I would recommend who can afford to work at that fee.
Recommending bottom feeders and wannabees can only hurt my business.
Not every desire warrants fulfilling.
I tried that, "All I have is $X" crap at a Guitar center and the salesman, after he was able to compose himself and stop laughing, finally told me he had to go rearrange the mark-a-lots- they use to make the LOWEST PRICE GUARANTEED signs.