I think I have seen somewhere that it takes about an hour and a half to walk from the road closed sign. It is the CHP who come up once every several years to pass out tickets, often just before the road crews open the road -- in May.
Like fish said: Don't venture past unless the forecast is perfect. If you need chains, don't go past.
Whitney Portal Hostel is the best for inexpensive. Bunk beds in a shared room. It is fairly new, and is clean and tidy. If you want an entire room, any motel will do.
My favorite breakfast is the Alabama Hills cafe, across the street from the Hostel. Pizza factory is great for dinner.
