Can my landlord legally give me 10 days to move out if I have 2 small children and I pay my rent on time?

Under the laws of all states in this country a landlord who wishes to evict his or her tenant is required to give at least thirty (30) days notice of the termination of the lease assuming there is a justifiable reason for such ending. As such, the ten (10) days notice is not adequate. I suggest that you consult with a family law attorney about your matter.