Loss of oxygen?

I turned on my TV last night and "Ghost Whisperer" was on. I'd never watched the show before, but I decided to leave it on anyway.

Basically, a plane crashes because the cabin loses pressure at a really high altitude and the oxygen flow doesn't work. Apparently the pilot forgot to check this in the pre-flight inspection. Everyone loses conciousness from lack of oxygen, gets cold and dies.

So, my question is, would this really happen this easily? I'm not doubting the science of it. However, I'm wondering if real pilots have no further recourse. In the show, they said that a person has about 20 seconds to do something before becoming too disoriented from lack of oxygen. It would seem to me that pilots should have an independent way of getting oxygen. Wouldn't it make sense for them to have a separate oxygen tank and mask that wouldn't be affected by plane-wide malfunctions?

Does anyone out there know what the actual situation is?