So far my search has been futile. Hostelworld shows me a hostel called HI Whistler Backpackers, but it is around 30 minutes away by bus from the closest skiing gondola. There's also a place called Pangea Pod Hotel, but they charge 150+ CAD for a bunk in a 36-bed dorm. It seems as if the cheapest option is to just drive back to Vancouver at the end of the day, rather than staying at local hotels.
Perhaps I'm missing something and there's indeed a budget option somewhere in Whistler?