The other answers focus on the physiology of failing to put a mask on, but I am going to offer another take on this.
Whether you die from not putting on a mask depends on one thing: Did the pilots get their masks on before useful consciousness ran out? If they did, you live. If they didn't, you die. It is as simple as that. In the case the pilots get their masks on and no one else does, they will initiate an emergency descent. This descent is typically initiated from memory items and not a checklist, so it can be initiated quickly. The goal of the emergency descent is to be at 10,000 ft iASAP (for us the goal was under 4 minutes), and many jet aircraft can get there faster. The only regulations I am aware of regarding the descent is that you must be below 25,000 ft in under 2 minutes (25.841; assuming complete loss of cabin).
If the emergency descent is initiated and in all likelyhood it won't matter if you put the mask on or not, you'll wake up during the descent and it'll only have been a few minutes. Its always better to put the mask on, but it won't be the deciding factor, the pilots masks will be.
I'll also point out the O2 masks the pilots have are vastly different than those the passengers get. Pax get chemical O2 generators that last about 15 minutes once activated (by pulling the tubing down) and attatch with a flimsy rubber band. The pilots get quick-don masks fed by an O2 cylinder. To don the masks you simply grab it, the O2 pressure inflates the webbing around the mask. Then you slip it on your head, let go of it and the mask compresses around your face. Twist the mask regulator to Emergency and you have positive pressure forced flow O2 for the descent.
§25.841 Pressurized cabins.
(a) Pressurized cabins and compartments to be occupied must be equipped to provide a cabin pressure altitude of not more than 8,000 feet at the maximum operating altitude of the airplane under normal operating conditions.
(2) The airplane must be designed so that occupants will not be exposed to a cabin pressure altitude that exceeds the following after decompression from any failure condition not shown to be extremely improbable:
(i) Twenty-five thousand (25,000) feet for more than 2 minutes; or
(ii) Forty thousand (40,000) feet for any duration.