Can beggers be choosers? Depends on what we're talking about. If we are referring to love and relationships, why should anyone beg? No one should just "settle" on someone if they don't feel that special connection or if important needs aren't being met. That's what deal breakers are. It's not fair to you, and not fair to the person being "settled on".
However, I also don't think people should have such high expectations that no one could ever fill them. Everyone is flawed in some way, and to think otherwise is being ignorant or naive.