In one of the recent episodes of the apprentice one of the candidates was heard bad mouthing the leader on the task to other team members. Donald rightly pointed out that this kind of behavior is destructive to the cohesion and productivity of the team. This kind of talk, even from someone who is ill respected on the team will undermine the leadership and cause decisions to be second guessed.
People are inherently positive or negative by nature. The positive person will most likely propose solutions instead of harping on problems. Hire the positive person and dispense with the problems that come with having negative people. Make it clear to everyone that you deeply value their opinions, encourage problem solving, and keep an open door policy.