Maybe there was some kind of problem with medication one time so they simply put a stop to it altogether. It's probably some kind of liability issue. I'm also assuming they don't have any kind of school nurse?
LIke somebody else suggested, I'd make sure you talk to the top person. Be sure you're getting the right information. Are they saying no because it's an actual policy or they just don't want to deal with it?
If they refuse, I'd look into other daycares. It might be hard at first, but at least you'll have somebody who is willing to give your daughters treatments if needed. You don't want to be in the middle of needing the nebulizer around the clock and then trying to find somebody else. I'd also call around to make sure this isn't something happening at all daycares. Maybe there's been a change in laws or something.
Also, my ds has had to use a nebulizer off and on. After a few times, I didn't have to sit there with him the whole time. I'd turn it on and hand him the mask. I'd still keep an eye on him to make sure he's holding it up to his face (he didn't like the strap around his head). So if your girls can do that, that might be worth mentioning.
L.