However, their inability to enact a new charter schools law in 2012 shows it's easy to talk about ambitious plans and difficult to round up enough votes to challenge the status quo.
Republicans control both chambers of the Legislature and seven of eight statewide offices. Still, party members aren't monolithic in their ideas about the best approaches for developing young minds. Some of the strongest resistance to charter schools in 2012 came from reliably Republican DeSoto County, which has the state's largest and fastest growing school district.
The Republican majority in the Legislature also can expect disagreements from Democrats, teachers' organizations, school administrators and advocacy groups that have different ideas about how to improve public education.
Statewide elected officials appeared before hundreds of business people this past week at Hobnob, a social gathering hosted by the Mississippi Economic Council.
Bryant advocated merit pay for teachers and said charter schools are "desperately needed," particularly in failing districts. Charters would allow parents, or others, to take over existing public schools and restructure them to provide a particular academic focus or disciplinary approach.
"I'm a disciple," Bryant said. "I've been to Helena-West Helena, Ark. I've been to New Orleans. Those systems work."
Lt. Gov. Tate Reeves said the Senate will push for "meaningful school choice legislation, including public charter schools." He said he wants to eliminate the process of electing superintendents, still used in about half of Mississippi's school districts.
Moving to appointing all superintendents is not a new idea. Lawmakers can expect pushback from people who think electing the superintendent provides accountability. Critics say elected superintendents don't necessarily need the top academic or management credentials.
Reeves said Mississippi needs to set higher goals for academic attainment.
"If you raise the level of expectations on administrators, on teachers, on parents and on our students, most importantly, they will rise up and meet those increased levels of expectations," Reeves said.
House Speaker Philip Gunn of Clinton said he wants public school choice.
"You get to pick what doctor you want to go to. You get to pick the mechanic. You get to pick the dry cleaners. You get to pick your church," Gunn said. "But yet we tell our children, 'You've got to go to this particular school, and if that school doesn't provide what you need, you have no other choice.'"
Gunn won't have to go far to encounter resistance. Clinton has a strong system of public schools, and local residents have shown a willingness to pay for top-notch academic and athletic facilities. Parents and administrators are likely to be skeptical about influx of students from other places.
Though it wasn't mentioned at Hobnob, critics also see school choice as a code phrase for re-segregating public schools.
Attorney General Jim Hood introduced himself to the business crowd by saying: "I'm your token Democrat."
He noted that MEC advocates early childhood education as a way to improve Mississippi's long-term economic prospects.
"We're going to have to have the fortitude to fund issues like early childhood education," Hood said. "And if those members who you've helped get elected refuse to do it because they're scared of some wing nut over in the tea party for having to raise revenue to help fund early childhood education, then you need to move them out of the way next election cycle, because that is the most important investment that you will make."
Follow Emily Wagster Pettus on Twitter: http://twitter.com/EWagsterPettus