Children's Act of 2010 - Establishes the National Council on Children to: (1) study and report to the President and Congress on the health, safety, and learning needs of children; (2) examine systems for children's programs and assess ways to increase spending in preventive services for children and youth in order to improve outcomes; (3) build upon the evaluations of other entities and avoid unnecessary duplication; and (4) make recommendations to improve children's well-being.