Both can be correct. It depends on how you see the family. If you see them as individuals, it's need. If you see them as one unit it's needs.
Writers are sometimes unsure whether to treat a collective noun as singular or plural. In fact, a collective noun can be singular or plural depending on the sense of the sentence.
>> That team is the worst in the league.
("team" treated as singular)
>> The team are not communicating amongst themselves.
("team" treated as plural)
When the group is considered as one unit, it is singular. When the individuals of the group are considered, it is plural.