The claims that Obama doesn't lead are wrong and muddle things.
The leadership critique obscures the real questions that should be asked about the sitting president or the person who wishes to replace him. Simply being a leader doesn't tell you much. George W. Bush used to say "a leader leads" as if simply taking action should absolve him of criticism. That didn't get him off the hook any more than Obama should be off the hook now.
The questions should be about effective leadership. Does he pick the right fights? Does he have the skills to succeed, or at least mark up a qualified success? If his leadership has not been effective, is the president the only one to blame? America does have a divided government. The president is not king. Is it Obama or Republicans in Congress who deserves the greater share of the blame? Or, as Christie suggested in his speech, is it both?
Getting the definition of leadership right keeps us from falling under the spell of pretty words. Calling for leadership is a trick both parties use to arouse anger and keep us from thinking too much more about the underlying issue. If only we had a leader, everything would be solved, they'd like us to think. But we should think more about what it actually takes to be president—what kind of leadership works and what kind of leadership doesn't.
Simply saying things aren't working and drawing a line back to whoever is president doesn't actually tell us anything useful that we might apply to the next person we'd put in office. Instead, we wind up voting for the person who most forcefully claims the current occupant lacks leadership. That makes for appealing speeches, but a fondness for rhetoric is what the president's critics say led the country into voting for him in the first place.