The list of people who may fill that role also includes Trump's son, Donald Trump Jr., as well as Sarah Palin, Arizona Gov. Jan Brewer, Oklahoma Gov. Mary Fallin and Continental Resources CEO Harold Hamm.
A bill introduced in the US House by Wyoming's Representative Cynthia Lummis would allow parents to have more choices of where their child could go to school.
Tyrrel announced his candidacy in front of his Charlie T's Pizzeria in downtown Casper in November, and cited his grass-roots, common-man background as a reason to vote for him.
Cheney is running for Wyoming's lone seat in the U.S. House of Representatives, which will be vacant when Rep. Cynthia Lummis leaves office at the end of her term.