Two lawmakers — both sitting on the influential budget-writing Joint Finance-Appropriations Committee — are looking at the wide-open and ever-changing race for state superintendent.

Here’s the rundown from a busy day on the election front:

Rep. Jeff Thompson: The Idaho Falls Republican told Idaho Education News’ Clark Corbin that he has been encouraged to run to by his constituents and supporters.

“I’ve had many people approach me about running, and based on that I am considering it,” said Thompson, who has has not filed campaign paperwork.

Thompson carried the K-12 budget bill on the House floor the past two sessions. One of his major legislative priorities this year is pushing to reverse recession-era cuts to school districts’ operational budgets.

Thompson has worked as a consultant for Idaho National Laboratory, as well as a regional manager for five Western states that allowed him to work with school districts, universities and local businesses.

Thompson’s wife, Chanin, has worked as a teacher and school counselor for more than 16 years.

Thompson also serves as vice chairman of the House Business Committee.

Sen. Steven Thayn: The Emmett Republican has had a change of heart — partially, at least.

For months, Thayn had ruled out a run for state superintendent. But that has changed with incumbent Tom Luna’s announcement that he will not seek a third term.

“I am considering it,” Thayn told Idaho Education News this morning.

Thayn says he has had between 15 and 30 people approach him about running for state superintendent. He expects to make a decision shortly — before Republicans and their top-of-the-ticket candidates go on their annual Lincoln Day banquet circuit. He’d also like to decide so potential state Senate candidates can consider a run.

“I think it’s important to announce sooner than later, so people can make those decisions,” Thayn said.

Thayn represents a sprawling legislative district that takes in Gem, Valley, Custer and Lemhi counties.

The candidate filing period, for statewide and legislative candidates, runs from March 3 to March 14.

Melinda Smyser: Widely viewed as a candidate in waiting, the former state senator says she is happy in her current job, heading Sen. Jim Risch’s field office.

“ … While I am flattered that (current Superintendent Tom Luna) and many others would feel I am qualified to take on the challenge of succeeding him in this office, I am going to … decline the opportunity,” Smyser said in a statement to the Idaho Press-Tribune.

Smyser has been a popular name in the election rumor mill for months, but the speculation surrounding the Parma Republican picked up this week. In announcing his plans to step aside after his current term ends, Luna dropped Smyser’s name, saying he’d had “conversations” about her running for the post. but ducked out before reporters could ask her about running.

Smyser, a former school counselor and Parma School Board member, served in the state Senate from 2008 to 2012.

Smyser’s decision, and Luna’s, leave two Republicans in the superintendent’s race: Grangeville teacher John Eynon and American Falls principal Randy Jensen. Democrat Jana Jones, a former deputy state superintendent and 2006 superintendent’s candidate, has announced her plans to run again.