The children ran into the school to tell teachers that a car had hit Nill, KCUR reported.
He later died of the injuries he suffered in the crash.
"He gave his life for the kids today," Fithian told KCUR.
Police said the driver, who was not identified, stayed at the scene, KMBC reported. He was later taken to an area hospital, KCUR reported.
"We don't know if it was speeding, distracted driving or some type of intoxication was the factor," Officer Jonathan Westbrook told KCUR.
The children Nill saved received counseling Tuesday before they went home with their parents.