The family met with the leader Friday after Davis was shot point-blank in the head by 18-year-old Karl Pierson at Littleton Adventist Hospital.
Hickenlooper stopped by the hospital again Sunday to check on her condition -- which was critical after undergoing surgery -- though he didn't see Davis.
"People are resilient and they push back, they don't accept it," Hickenlooper said. "If nothing else it really does teach you to love your family and love your neighbors, in a funny way it pulls people together in a very powerful way."
"She was just a very sweet girl. She's really smart," classmate August Clary said. He said Davis loves to ride horses and "wouldn't hurt a fly."
"Our beautiful daughter, Claire Davis, has severe head trauma, as the result of a gunshot. She needs your continued prayers. We would like to thank our family, friends, the community and the equestrian community for their outpouring of love and support, as well as the school for their continued support of the students and teachers," the girl's family said in a statement.
Officials don't believe Pierson had any reason to shoot Davis, who he encountered in the school's library while he was looking for school librarian and debate coach Tracy Murphy. After shooting Davis, Pierson shot and killed himself.