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?
I've asked around and the answer is that the two hostels I've mentioned (HI Whistler Backpackers and Pangea Pod Hotel) are pretty much the only options under $100/night in Whistler.
Therefore I've chosen to just drive from Vancouver to Whistler and back. It's less than 2 hours most of the time and since the gondolas close at 4pm there's really no point in staying too late. For visitors from outside of Vancouver staying at the HI hostel is probably the best option, especially if you have a car and don't have to wait for the bus.