This is flatly false. When Obama took office the debt stood at $10.6 trillion. After inheriting two wars and the worst economy since the Great Depression, the debt has grown by $3.7 trillion since Obama has been in office. Palin is off by about $7 trillion.
So not only has the debt not increased more under Obama than all other Presidents combined, it has increased less under Obama than our last president, George W. Bush. Under President Bush, who inherited a $236 billion budget surplus from President Clinton, the deficit increased by $4.9 trillion.