We're quite regular fliers into gib and unfortuantely theres not a great choice of car hire companies operating out of the airport cos its so small, 2 I think, one being aurigacrown (who we generally use) and I think the other one was europacar, but not 100%.
I tried to book a car for some friends a couple of weeks ago who were also flying into gib and they had came up with nothing - no cars available at all. (I believe there was a thread somewhere about auriga not buying any more new stock and running out of cars - not sure if that was something to do with it). I tried for them too and was getting the same problem so I e-mailed auriga and asked if they had anything available at all. They informed me that they had a choice of about 3 cars available, cant remember how much, it was only for three days hire, but at least our friends got a car. You pay at the airport and have to have your card swiped as a deposit for damages, fuel - we pay for a full tank but return it empty, cant say we really have that much of a problem with them, but then others will disagree!
Unfortuantely leaving it at such short notice will always be a problem, especially at this time of year and the companys know that youre desperate and will try to charge you the earth. Depending where youre staying, you could consider getting a taxi to your hotel (if thats what youre staying in) and asking the conceirge to sort you one out, or if your staying in an apartment there are car hire places around that you can walk into and try your luck there.
Dont know if this has been any help, best of luck and have a great time out there!