Devil's Advocate - giving the venue the benefit of the doubt, maybe they didn't push the issue in the past, but maybe they very-recently got busted by the their city for not requiring their vendors have a license. I'm sure there are consequences for them allowing non-licensed vendors, just as there are consequences for you for doing business in an area that requires you to be licensed. it's not up to us to pick and choose what laws we follow, you shouldn't expect the venue to do the same and make exceptions because you don't like them. You know what I mean?
Bottom line - If it's a city/county requirement that you pay a fee for doing business in their area, it's not the venue's fault for following it.
As a business person, I wouldn't be mad at anyone but myself. As harsh as this may sound, it's nobody else's responsibility but yours to make sure your business is legal and has all the appropriate permits, licenses, insurance etc. It ain't the venue's responsibility. Sure, I'd be irritated, I may even be pissed because obviously I wouldn't be the only one looking like a dope right now, but I'd put on my professional "I Got This Covered, Bride, And You Have Nothing To Worry About" face.
You quite possibly are in in breech of your own contract by not being licensed in that area. My contract is pretty extensive, but "not being licensed and not having the money to pay for it" or "I don't want to pay for the license because I don't see the monetary benefit" aren't cancellation exceptions. Earthquake? Yes. Zombie Apocalypse? Yes. Don't want to get the license for the area in order to fulfill said contract? No.
So think about how the bride, in a hyper-sensative over-emotional state- is probably perceiving YOU (everyone) right now - I can only put myself in her place - but honestly I'd be thinking that all the businesses I contracted with that don't have licenses to do business where my wedding is are complete idiots, and anyone that isn't doing whatever they need to do to be legal this late in the game would not only never get my business again, but I'd never refer business to them ever and quite possibly blame them for ruining my wedding. I'd be thinking, you are the professionals that do this all the time, how could you not know? And if a vendor asked me, the bride, to pay the fee, I'd go from freaking out to nuclear. I'd probably call you very colorful names and tell you to go fornicate with yourself, followed by telling you that I expect a cake to be delivered per our contract otherwise I'll sue the poo-poo out of you.
Sounds harsh - but this isn't a normal person you are dealing with, you are dealing with a bride.
So, if I were you, I'd find the money and pay the fee ASAP with a smile, then start advertising "Licensed to do business in XXX!" to compensate for it.