Here are the references for this Mayo Clinic article that talks about 2 hrs of screen time. It is not just a made up number.
Children and TV: Limiting your child's screen time - MayoClinic.com
References
Christakis DA, et al. Television, video and computer game usage in children under 11 years of age. The Journal of Pediatrics. 2004;145:652.
Dennison BA, et al. Television viewing and television in bedroom associated with overweight risk among low-income preschool children. Pediatrics. 2002;109:1028.
The benefits of limiting TV. American Academy of Pediatrics.
HealthyChildren.org - The Benefits of Limiting TV. Accessed Jan. 7, 2011.
Jordan AB, et al. Reducing children's television-viewing time: A qualitative study of parents and their children. Pediatrics. 2006;118:e1303.
Ginsburg KR, et al. The importance of play in promoting healthy child development and maintaining strong parent-child bonds. Pediatrics. 2007;119:182.
Thompson DA, et al. The association between television viewing and irregular sleep schedules among children less than 3 years of age. Pediatrics. 2005;116:851.
Borzekowski DLG, et al. The remote, the mouse and the No. 2 pencil: The household media environment and academic achievement among third grade students. Archives of Pediatrics & Adolescent Medicine. 2005;159:607.
Zimmerman FJ, et al. Early cognitive stimulation, emotional support, and television watching as predictors of subsequent bullying among grade-school children. Archives of Pediatrics & Adolescent Medicine. 2005;159:384.
Media education: What parents can do. American Academy of Pediatrics.
HealthyChildren.org - Media Education: What Parents Can Do. Accessed Jan. 7, 2011.
Laurson KR, et al. Combined influence of physical activity and screen time on recommendations on childhood overweight. The Journal of Pediatrics. 2008;153:209.
Broughton DD. Keeping kids safe in cyberspace. AAP News. 2005;26:11.
Children, adolescents and television. American Academy of Pediatrics Committee on Public Education. Pediatrics. 2001;107:423.
Page AS, et al. Children's screen viewing is related to psychological difficulties irrespective of physical activity. Pediatrics. 2010;126:e1011.
Sege RD. Television and media violence.
UpToDate Inc.. Accessed Jan. 5, 2011.
Christakis DA, et al. Preschool-aged children's television viewing in child care settings. Pediatrics. 2009;124:1627.
What children are not doing when watching TV. American Academy of Pediatrics.
HealthyChildren.org - What Children are NOT Doing When Watching TV. Accessed Jan. 7, 2011.
Swing EL, et al. Television and video game exposure and the development of attention problems. Pediatrics. 2010;126:214.