Michelle, I won't be as positive as saltydog. It may be possible, but only for a few.
Whitney can be done as a day hike hike when the trail is nearly snow free, but in mid May, that won't be the case. You will have maybe a third of the distance through snow, though there will be tracks through it, so much of that will be consolidated.
You can do it if you are in really great shape -- if you hike regularly and are in top aerobic condition, then you have a fair chance of making it. If your condition is less than that, you should go, but as salty recommends, stick to your turn-around time.
You will want to get a super early start -- 3 or 4 AM might be good.
Do not worry about permits -- mid May is so early that few people will be hiking, due to the extra snow.
