"What it tells me is that people have different skill sets at different times," Christie said.
The audience laughed.
Stewart responded: "I see. So, he wasn't a leader until you needed leadership?"
"Maybe until until he was presented with a stark opportunity to lead," replied Christie.
Christie and Stewart covered a lot of ground during Thursday's interview, ranging from the impact of Sandy to health care policy.
Next Wednesday, Newark Mayor Cory Booker (D) -- Christie's friendly rival and potential gubernatorial opponent -- will appear on "The Daily Show."
Check out the Christie interview below. The exchange about Obama comes toward the end of the first clip.