She is in "very critical condition," Arapahoe County Sheriff Grayson Robinson said Sunday.
Davis, a 17-year-old senior at Arapahoe High School in Centennial, was shot in the head Friday by 18-year-old senior Karl Pierson, who fired several random rounds in a school hallway before shooting Davis.
Robinson told reporters Davis appeared to have been a random victim.
Seconds later, Pierson turned the gun on himself. Officers found his body in the school library.
Robinson said Pierson had expressed threats against school librarian Tracy Murphy to other students and was targeting Murphy in the shooting. Murphy is also the debate coach.
Murphy was able to safely leave the school, authorities said, a decision they said may have averted further violence.
Pierson had stormed into the school shortly before 12:30 p.m. with a pump-action shotgun, a bandoleer of ammunition, a machete and three Molotov cocktails.
The school, 13 miles south of Denver, is also about 8 miles from Columbine High School, site of the April 1999 mass shooting by two 12th-grade students who killed 12 students and a teacher and injured 24 other students. It is also near the Aurora, Colo., movie theater where a gunman killed 12 people and shot 70 others in July 2012.
Friday's shooting occurred a day before the one-year anniversary of the mass shooting at Sandy Hook Elementary School in Newtown, Conn., that left 20 schoolchildren and six adult staff members dead.
Pierson bought the shotgun a week before the shooting and later bought the ammunition, as he was entitled to do under Colorado law, the sheriff said.
Investigators have spoken with Murphy extensively and are beginning to understand the relationship between the two, Robinson told the Denver Post.
"We're beginning to better define that, but at this point in time it's not something we're going to talk about," Robinson told the newspaper.
Robinson and Gov. John Hickenlooper credited the swift response by a deputy sheriff working as the school's resource officer during the shooting.
"This could have been much, much worse," Hickenlooper told CBS' "Face the Nation."
Hickenlooper said he also visited Davis and her family Sunday.
"We all have to keep Claire in our thoughts and prayers," he said.
Robinson told reporters Sunday investigators had wrapped up their investigation and released control of the building back to the district at 6 a.m. Monday.
The school, normally open for students to study before finals this week, will remain closed until after the New Year.
Students would be allowed to return to school to pick up personal belongings Thursday or Friday, depending on what grade they are in, the principal said in an email to parents.