Bees can only survive about 3 weeks without a queen. If they are unsuccessful in raising a new queen on the first try, they will be in very severe danger of dying. After about 3 weeks without a queen a hive will begin producing laying workers See: Laying Worker. Laying workers can only produce drones- which are useless to the hive.
Hopefully, when you discover your hive is queenless it will have been less than two weeks.
What to do…
There are several different clues that will tell you how long the hive has been without a queen. If there is still some young brood it will have been less than a week and a half.