It will not be just a matter of endurance.
Rather, it could be very dangerous, especially if you are not skilled w/ an ice axe and crampons. I decided against hiking on June 1 due to the trail being covered w/ ice, and after reading for weeks of people trying to go up, or down, the steep "chute" (to avoid the ice-covered switchbacks) and often falling and tumbling down several hundred feet and injuring themselves and others. If you are not familiar w/ the chute, it is a very steep slope (probably about 40 degrees incline) that takes you directly from Trail Camp to Trail Crest, a vertical gain over 1000'. It is not used by hikers once the snow melts, as then the less steep switchbacks are used.
Anyway, those are my thoughts.