That buzz grew louder after Lockhart's speech on the opening day of the 2014 Legislature when she took aim at Herbert, calling him an "inaction figure."
But, sources tell me, polls showing Herbert with a nearly 70 percent approval rating, his ability to amass large amounts of money through the annual Governor's Gala and other events, and his pending elevation to chairman of the National Governors Association have convinced Lockhart that her chances of unseating the incumbent at the 2016 Utah Republican Convention are slim.
Earlier this year, Lockhart unveiled a bold initiative to put an electronic device, such as a laptop or a tablet, in the hands of every public school student in Utah. The estimated price tag: $200 million to $300 million. The speaker said it was worth it because it would move the state's education system into the 21st century. Her plan fizzled, but she predicted such a dream eventually would become a reality.
The superintendent's job became available with Martell Menlove's recent decision to retire earlier than he had anticipated. That move was prompted by perceptions of hostility from some board members toward the Utah Office of Education and an audit committee meeting in which Menlove and other staffers were ordered to leave.
Menlove and Deputy Superintendent Brenda Hales announced they were leaving soon after that meeting.
In another bizarre twist, the board's two leaders, Chairman David Crandall and Vice Chairman David Thomas, named Joel Coleman, superintendent of the Schools for the Deaf and the Blind, as interim superintendent without a board meeting or vote.
Coleman is a former state board member who worked in the LDS Church's seminary program. His wife, Kim Coleman, directed a charter school, the Monticello Academy. She eventually was forced out of that job by the State Charter School Board and is suing the board and members of the Utah Office of Education over that action.
After Joel Coleman's selection as interim boss, protests from some board members prompted the call for a special meeting of the panel to discuss the appointment.
Coleman has said he has no intention of applying for the permanent post and would serve only until the board hires a full-time leader.
Another applicant for the job is Rich Crandall, a former Arizona state senator and state school administrator in Wyoming who has since moved to Utah. He reportedly is good friends with Lockhart.