UPDATE
After a bit of phone tag with the El Paso Advantage car rental office, I finally got a car through them, same deal as Mel and Nathan. However, I had to go through the manager Deanna(sp??) and had to beg her. She was great and hooked me up. Bottom line, she said they were only going to allow a set number of cars to be picked up/dropped off at the airport and they have reached that limit so no more as of today. You can still rent from them but you can't drop it off at the airport on Sunday.
However, Enterprise will now allow you to pick up and drop off at the airport but it's a bit more expensive, $26 a day and they'll charge you through Monday. So that's a total of $78, not sure if tax is included.
I'm assuming there will be plenty of cars at the airport so I'm sure we can get everyone to the motels if someone does end up without a car.
Hope this helps.