As with many things, being firm and positive is a must. A clear deadline of two or three months would be helpful for many to understand and make their plans accordingly. America is not like many parts of the world where it has long been the tradition that several generations or families live under one roof.
Many people in America don't realize all the stresses that come with living with others until they actually do. Once the adult children move from the nest, the parents can breath a sigh of relief and fully relax in their own home again, and they begin to savor the fact that there is nothing like having their own.