He really isn't. Some aspects of his administration are centrist-liberal (see: healthcare reform), and maybe to the largely-very-right-wing mainstream political sphere of the USA he's a leftist, but on the global stage Obama is pretty firmly in the center.

Obama's healthcare reform is almost exactly the same plan the Republicans advanced as the conservative alternative to Hillarycare in the 1990's.

On the other hand, he did nationalize two car companies....

He's campaigned for more extensive reforms than what actually took place - I'd place his position further left than the current state of health care.

That said, mainstream politics in the US has shifted dramatically to the right since the 90s. The conservatism of the 90s is the "liberalism" of today.

This, basically. America as a whole is pretty far right. When you're left of that, it's not very left at all.

On a global scale, these "left" / "right" labels lose a lot of their meaning and are more a sign of a poorly framed discussion than a useful shorthand.

Reconcile to "right" and "left" say, at-will employment, or a right to bear arms, or mandatory health insurance, or laws prohibiting Nazi sympathism, or vigorous loser-pays libel laws, or tax-free churches, or the right to keep and bear arms... the list goes on and on. The US is statist is some ways that Europe isn't, and libertarian in others.

At the end of the day, these things all boil down to differing priorities and to different levels of policy sophistication.