Unless you manage to make an enemy of a member of faculty, in which case you are generally and fully boned. I've met people who had this happen, and generally the best thing to do is just to leave and get a degree elsewhere. The other reason that policy doesn't get waived is if people really don't think you're qualified for the degree, which means they follow the policy so as to not get sued. I knew a guy who tried suing the university over this, and let's just say life has not gone well for him.

It also might work to get the PoliSci professor on the committee if the department chair or department's graduate chair approves. If it doesn't get resolved quickly, don't be afraid to talk to people about it, especially people you already know. The folks at your division of graduate studies -- whatever it's called there -- might know how similar cases were handled in other departments. It's not as if small faculty sizes in the humanities are a new phenomenon, after all. Don't start from the "please fix this for me" mode, just ask if they have any ideas on how to proceed.