How long do I have to accept a dweller into my Vault?
Solution 1:
Wasteland Dwellers whom are on the outside of the vault waiting to get inside will stay forever until you accept them in or choose otherwise. Radio calls on the other hand can be accepted at any time just like any other resources (Stimpacks etc.); the downside being that anyone in the room stops gaining experience.
I know this based on my knowledge of the game. Hope it helped.