Will not listing references kill my chances of a part-time job?

I'm currently in a long-term job search for a professional position in my career field, which is very small and will probably take several months. In the mean time, I need a part-time job (or full-time entry level job) to pay for bills, etc. I'm applying at places like restaurants and retail stores, but some applications ask for references. I really don't want to have my professional references bothered for these part-time jobs on the off-chance that these companies call them, but I also have a very limited social/professional circle so I have no other references to list. If I don't list references, will my application just be thrown out? Should I just list the references and hope that they are not called?

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