Did President Obama win Georgia state?

No, in the U. S. Presidential / Vice Presidential election of 2008, all 15 of Georgia's electoral votes went to John McCain and Sarah Palin.

2008 Georgia Popular Vote:

• 52.10% - John McCain / Sarah Palin
• 46.90% - Barack Obama / Joe Biden
• 1.00% - others

In the 2012 elections, all 16 of Georgia's electoral votes went to Mitt Romney and Paul Ryan.

2012 Georgia Popular Vote:

• 53.19% - Mitt Romney / Paul Ryan
• 45.39% - Barack Obama / Joe Biden
• 1.43% - others