Covey has largely been sedated but has been able to respond to commands from the medical staff at Utah Valley Regional Medical Center, his daughter said.
"He's still in the ICU," Sagers said. "It's still pretty scary right now. [Family is] just praying a lot he's OK.
"They're just waiting to see if the brain is going to swell and bleed out more," Sager added. "And if it [bleeds] out more they'll probably have to go in and drain it."
Sagers said her father, an avid cyclist, was cycling with a friend Thursday in Rock Canyon Park when the accident occurred.
Covey went down a hill too fast and flipped forward on the bicycle, Sagers said. She said her father was wearing a helmet but it appears to have slipped backward as Covey was falling. Covey's head hit the pavement, Sagers said.
"It was a pretty big goose egg on the top of his head," Sagers said.
Covey also suffered cracked ribs and a partially collapsed lung. The friend called 911, and an ambulance took Covey to the hospital.
The lung injury has required doctors to put a ventilator tube in Covey's mouth, Sagers said.
Sagers complimented the response of the EMTs and the hospital staff. Family gathered at the hospital on Thursday night.
"Last night we had so much family in the waiting room, there was probably 35 people," Sagers said.
Covey was a Brigham Young University business management professor when he became a household name with the publication in 1989 of The 7 Habits of Highly Effective People.
The book made him highly successful, selling more than 10 million copies with editions in 40 countries in 28 languages.
He became a management guru for companies and agencies such as Saturn, Ritz Carlton, Proctor and Gamble, Sears Roebuck and Co., NASA, Black & Decker, Public Broadcasting Service, Amway, American Cancer Society and the Internal Revenue Service.
The book was the catalyst for his Covey Leadership Center in Orem, with 40 offices worldwide that sold books, tapes and videos and produced conferences where Covey talked about his approach to management. In the 1990s, the business had tens of millions of dollars in sales per year.
Time magazine in 1996 named Covey one of its top 25 power brokers.
7 Habits was followed by First Things First, Principle-Centered Leadership; The Seven Habits of Highly Effective Families; The 8th Habit: From Effectiveness to Greatness; and The Leader In Me How Schools and Parents Around the World Are Inspiring Greatness, One Child at a Time.
Due out this year is The 3rd Alternative: Solving Life's Most Difficult Problems.
In 1997, the Covey Leadership Center merged with Franklin Quest, which sold a successful time management planner, to become FranklinCovey. It sold planners, consulting services and conferences.
Covey is a professor at the Jon M. Huntsman School of Business at Utah State University, where he holds the Jon M. Huntsman Presidential Chair in Leadership.
Covey earned degrees from the University of Utah, Harvard and BYU.
Tribune reporter Tom Harvey contributed to this story.