Many Democrats like to credit Barack Obama for stopping the massive job losses of 2008-09 and creating new jobs. Moveon.org did so here. They posted this chart:
Despite the convenient chart, it's completely unreasonable to give so much credit to Obama. The economy was not capable of continued job losses at those rates. Should Bush have served a third term, the above chart wouldn't look much different.
Additionally, Presidents simply don't have as much power as they are credited with. Just like their influence on oil prices are minimal, so are their influences on job numbers. It's actually the Federal Reserve and Congress that has more influence with the policies they set.
The real question about Barack Obama is whether he supported or opposed certain policies and how they affected employment. And the bottom line is that he, as most other politicians would have, made the problem worse. The "recovery" seen above is abysmal. The right policies would have unemployment rates at record lows already. And those policies are pretty much the opposite of what everyone in Washington advocates, Obama included.
Those policies are: reducing government interventions, i.e. free markets. The 1920 Depression is quite an impressive (though not perfect) example of that approach put in practice.