President Obama is the leader of the United States. That much is certain, despite the protestations of some.
But what is less clear is what it means to be president. Or in this case, to lead.
Looking at the Oxford English Dictionary's definitions (subscription required) for lead is somewhat instructive. The first definition is "To bring or take (a person or animal) to a place" is the most direct and literal/physical meaning.
The second definition is the one I find most intriguing--"to accompany and show the way to: to conduct, guide, esp. to direct or guide by going on in advance; to cause to follow in one's path."
This one and the fifth are the most relevant to the actions of a president outside of war (which is covered in the fourth definition). The fifth reads: "To guide with reference to action or opinion; to bring by persuasion or counsel to or into a condition; to conduct by argument or representation to a conclusion; to induce to do something."
Looking at the Oxford almost always surprises me, because it often reveals telling subtleties of language. In this case, the definition that focuses on accompaniment and showing--that leading is as much an act of being as it is showing. It's clear that part of Obama's mission is convince the country that improvement is on the way both through direct persuasion*, as highlighted in the fifth definition, and through his calmness.
In other words, leading is more than decision and speech making; it is indirect and subtle.
*This whole section focuses on the things the Obama administration is doing and has done.