While Jay Leno had a fake presidential interview on his first show Monday night, David Letterman will have the real thing September 21. President Barack Obama will make the first appearance ever by a sitting U.S. President on CBS’s Late Show with David Letterman on next Monday’s show. He will be the sole guest on the broadcast. President Obama has already appeared on The Tonight Show since being inaugurated in January, making a visit to the program, then hosted by Jay Leno, on March 19.