While being vectored during a busy lunch hour over Lambert, I heard a Cessna call approach and request vectors for touch and go's at STL. The controller was patient and explained that the airport was too busy to handle that request at the time. After a couple minutes, the guy again asked the controller for touch and go's at STL, and added that it was a public airport and they should make room for him. The controller responded, "Affirmative sir, turn direct to Foristell VOR and hold. EFC sometime tomorrow."