I can report from experience that the carb on an O-540, as used in the PA28-235, holds enough gas for a three minute ground run, a normal runup, and the beginning of a backtrack, having been cleared for take-off. Halfway through the backtrack the engine died. The fuel selector was off.
Then there is something wrong with your aircraft.
When we do C of A air tests it is a requirement to time how long it takes for the engine to stop using 1200 rpm with the fuel selected Off.
From memory if it is more than 2 minutes then it is a reportable defect.