Does it really happen so often that there's someone you'd hire, but they want more than your absolute max? In my experience, just FINDING good people is 95% of the challenge -- compensation is not a common-blocker to make it a first-round filter.

By having your recruiter filter resumes by comp, it may be that they're accidentally throwing out just those few resumes that were actually the strongest! Maybe you could have negotiated to a good number for both of you.