Republican David Vitter and Democrat John Bel Edwards are both Common Core critics, but uprooting the academic standards from Louisiana classrooms will be a huge challenge, whoever wins the governorship.

And replacing state Superintendent of Education John White, which Edwards has promised to do, will be even tougher.

“He can’t just wave a wand and make it so,” said Jim Garvey, who just won re-election to the state Board of Elementary and Secondary Education.

For Vitter and Edwards, who face off in a Nov. 21 runoff, one of their areas of agreement is that Common Core has to be drastically overhauled and newly designed state-crafted standards put in its place.

But the makeup of BESE and the rules for making major changes mean that both candidates face major obstacles if they are going to fulfill their campaign promises.

BESE has 11 members, including three who will be named by Edwards or Vitter. However, all six races decided in the Oct. 24 primary produced winners who back the Common Core standards, or something like them.

Former BESE member Linda Johnson, who lives in Plaquemine, said the vote sent a clear message.

“You look at the makeup of the board, and it is people who support Common Core,” Johnson said. “The people have spoken on that issue.”

The final two elected slots on BESE will be decided the same day that voters pick a governor. Both feature races where there are clear splits on Common Core, including the District 6 race in Baton Rouge to decide BESE President Chas Roemer’s successor.

Even if critics of the standards win both races and join forces with three gubernatorial appointees who want to overhaul Common Core, they would have a five-person bloc — one short of a majority.

In addition, an ongoing review of the standards by about 100 educators and others — the results will be forwarded to BESE — could have a big impact on what Vitter or Edwards demands in the way of changes.

Edwards told the Louisiana School Boards Association that he is concerned the review will produce simply a “rebranding” of Common Core under a different name.

Vitter told the LSBA that changes recommended by BESE have to meet three tests: No rebranding, they must prepare students for college and the workplace, and they must be verified as equally or more rigorous than the Common Core standards.

All of that is likely, said Garvey, who is vice president of BESE.

“We acknowledge that the current standards are not perfect,” he said. “I think the changes are going to be significant.”

Some critics of the academic guidelines already have charged that a whitewash is in the works.

Meanwhile, White has said he hopes to remain as superintendent, no matter who succeeds Gov. Bobby Jindal, a Republican.

Edwards has made clear that that will not happen in an Edwards administration.

“I have no intention of allowing John White, who isn’t qualified to be a middle school principal, to remain as superintendent when I am governor,” he said earlier this year.

Vitter has questioned whether White, who backs Common Core, is best suited to carrying out Vitter’s goals of remaking the standards in reading, writing and math.

Joshua Stockley, an associate professor of political science at the University of Louisiana at Monroe, said White gained job security with the election of six BESE members Oct. 24 viewed as pro-reform.

“That being said, I suspect an individual like David Vitter might exert a little more influence, a little more heavy-handed, over his long-term prospects,” Stockley said of White.

But it takes a super-majority of BESE — eight of the 11 members — to name a superintendent, meaning it is a huge task for even an arm-twisting governor to get his pick in the job.

In 2011, Jindal, who was about to coast to re-election, was unable to get White hired as superintendent. He then took the highly unusual step of getting involved in BESE races, backing five of six winning contenders and paving the way for White’s selection in 2012.

Garvey, a lawyer from Metairie, said picking a superintendent requires a super-majority in part to minimize the politics in a job that used to be an elected position.

“I think when you have 11 members picking the superintendent, rather than one governor, it helps get the politics out of it,” he said.

Former BESE member Leslie Jacobs, who lives in New Orleans, said things have changed from a time when the board routinely endorsed the governor’s candidate for superintendent.

“I think you will see a much more independent BESE,” said Jacobs, who served on the panel from 1996 to 2007.

Johnson was even blunter.

“I don’t think they have the eight votes,” she said. “If I was John, I would be real happy.”

Follow Will Sentell on Twitter, @WillSentell. For more coverage of Louisiana government and politics, follow our Politics blog at http://blogs.theadvocate.com/politicsblog/