Susana Martinez and Brian Sandoval were swept into office as part of the 2010 GOP wave — two Hispanic governors in Western states who each had the potential for political stardom.

Ms. Martinez has struggled in New Mexico, fulfilling her campaign promise of fighting against tax hikes but failing to get the state’s economy moving again. The unemployment rate has fallen just 1 percent since she took office in 2011 and is among the bottom third of the country.

Mr. Sandoval, meanwhile, is riding high in Nevada, politically speaking, despite — or perhaps because — he broke his no-new-taxes promise. His state’s unemployment rate, which topped out at nearly 14 percent in 2011, is now under 5 percent, and he’s managed to score some conservative victories on social policies like school choice.

Seventeen new Republican governors were elected in 2010 as part of the national GOP wave, and like their congressional counterparts, they promised to usher in a new era of booming economies, slimmer government and a bulwark against President Barack Obama.

Most have been successful in reviving their economies, and many made major strides in conservative policies such as limiting the power of public employee labor unions. But they’ve not always been rewarded by their own voters.

“The class of 2010 did very well. They put in place some substantial tax cuts,” said Chris Edwards, who studies state governors for the Cato Institute. But he added: “States get into fiscal trouble because of a lot of things outside of their control, like oil prices in a state that’s dependent on oil, like Oklahoma. Sometimes they have to do things that are unpopular to balance that.”

The wave of new GOP governors included a dozen who captured seats from Democrats or independents, including the big states of Florida, Ohio, Michigan and Pennsylvania. Five other GOP governors won seats that had been held by a Republican who was term-limited or lost in a primary.

Jon Thompson, communications director for the Republican Governors Association, said it was Republican governing in these states that helped President Trump take the White House.

“Without Scott Walker’s success in Wisconsin, Rick Snyder’s success in Michigan and John Kasich’s success in Ohio, it would have been a lot tougher for Donald Trump to win these states in the 2016 presidential election. These governors ushered in a new wave of Republican power, and it culminated with the election of President Trump to the White House in 2016,” he said.

Governors shot out of the blocks with a series of big promises.

In Wisconsin, Mr. Walker promised to bring the public sector labor unions to heel after a bitter battle that saw him have to win in the legislature, then in the courts, and then survive a recall election. Gov. John Kasich won a similar showdown in Ohio, though voters later overturned his new law.

In Iowa, Gov. Terry Branstad promised 200,000 new jobs by 2016. He and his critics debate whether he’s reached that goal, but as Mr. Branstad departs for a new job as the Trump administration’s ambassador to China, there’s little doubt the economy is humming: Unemployment in the state has shrunk from 5.6 percent to 3 percent.

Gov. Rick Scott also promised 700,000 jobs would be created in Florida, and he’s nearly doubled that, with 1.3 million private-sector jobs added between January 2011 and January 2017. Unemployment, which was a staggering 10.5 percent in January 2011, was just 5 percent at the beginning of this year.

Other GOP governors took on social issues, with Tennessee Gov. Bill Haslam pushing charter schools and Oklahoma Gov. Mary Fallin winning a bill pushing the state’s health department to create an “abortion-free society” curriculum for high school students.

In Michigan, Gov. Rick Snyder steered clear of hot-button issues, instead putting his effort into cleaning up the troubled city of Detroit. He put the city into managed bankruptcy in 2013, appointed an emergency manager to handle city assets and struck a deal with public-sector unions over benefits.

Within 16 months the city was out of bankruptcy, and Mr. Snyder gave talks around the country about how he achieved such a feat, even stirring up rumors of a presidential bid in 2016 that did not come to fruition.

Mr. Walker and Mr. Kasich did both mount presidential bids that stumbled, while South Carolina Gov. Nikki R. Haley, also part of the class of 2010, was mentioned as a potential vice presidential pick. Instead, she has become President Trump’s ambassador to the U.N.

The governors have struggled with some issues — including whether to embrace Obamacare’s expansion of Medicaid. Only six of the 2010 GOP governors agreed to some sort of expansion, while the others declined it, saying they feared putting their future budgets in jeopardy.

Of the 17 GOP governors newly elected in 2010, all but one won re-election in 2014.

Mr. Thompson said that it was Republicans’ economic agenda that brought them political victory.

“While Republican governors have been successful on multiple avenues of reform, a main focus was making their states strong engines of economic growth, and on that policy, they have exceeded expectations,” he said.

The exception was Tom Corbett in Pennsylvania, who faced challenges on both the right and the left in his state legislature. Mr. Corbett’s biggest downfall was slashing funding to public education, which Democratic challenger Tom Wolf hammered him on during the election. But his relationship with Republicans in Harrisburg was also frosty. He was the first Pennsylvania governor to lose re-election in over 40 years.

Alabama Gov. Robert Bentley also departed early, resigning earlier this year over reported ethics and campaign violations.

Most of the rest of the Class of 2010 is term-limited and unable to run again, save for Mr. Walker in Wisconsin.

Democrats say this is a good thing for them looking toward 2018.

“I think that in terms of popularity, in measures of how voters think about it, you’ve had GOP governors for eight years, and people are tired of those governors,” said Jared Leopold, spokesman for the Democratic Governors Association.

He said he’s seeing Republican candidates drift even further toward the right than their sitting Republican governors, something he thinks will turn off voters.

“What’s interesting in the 2018 class running to replace these guys is they’re far more to the right than these sitting governors,” he added. “The people of those states don’t believe those have been successful.”

Sticking to campaign promises hasn’t always been easy, however, nor has it been a path to political success. In Kansas, Gov. Sam Brownback pushed a major cut on personal income tax and eliminated income tax on profits for limited liability companies. The state has struggled with budget shortfalls and elimination of other services as a result.

His political standing is so low that analysts said it nearly dragged down the GOP candidate in a special congressional election earlier this year.

One difference between the successful and the struggling governors is the nature of the legislatures they deal with.

Voters tend to reward governors who find ways to work with their statehouses, said Nathaniel Birkhead, a professor at Kansas State University who studies state legislatures.

“Governors might be better off to find balance with legislators of [a] different party,” he said. “While we expect fidelity to campaign promises, we tend to reward those who compromise.”

Even those states where the legislature is controlled by the same party as the governor can prove to be obstacles, particularly when the legislatures are considered strong compared to the chief executive.

In Nevada, for example, Mr. Sandoval wanted to enact major tax cuts to help fund his public education program, but the state legislature forced him to negotiate. He ended up agreeing to extend existing taxes that had been set to expire during his term.

Mr. Sandoval later agreed to the largest tax increase in the state’s history, yet remains one of the most popular governors nationwide.

Jon Ralston, a top political analyst in the state, said Mr. Sandoval did pursue conservative policies such as school choice, but the tax battle overshadowed that. Fortunately for Mr. Sandoval, he’s been blessed with a business climate that’s attracting major businesses to the state, thereby boosting his standing.

It doesn’t hurt that he’s also been able to charm his legislature and his voters.

“The guy is just so likable in addition to getting so much done,” Mr. Ralston said. “Even though he passed the largest tax increase in state history, with a Republican-held legislature, he remains one of the most popular governors in the country. Who else could do that?”

Ms. Martinez, meanwhile, has faced a Democratic legislature and frequently battled it.

She upheld her campaign promise of not raising taxes, even vetoing the legislature’s budget in April because it called for tax hikes. Lawmakers sent her a new bill last week with more taxes — something the governor has said she will not support.

“I think I could say that, as far as I can tell, New Mexicans would have been more satisfied if the governor had found a way to cooperate more,” said local pollster and analyst Brian Sanderoff. “People get tired of the gridlock and fighting. They have worked together on some issues, and she’s found success there.”

One such area is the voter ID law that restricts illegal immigrants from obtaining a driver’s license. Ms. Martinez repeatedly pushed the issue, which finally passed in 2016 with the cooperation of the state legislature.

Part of Ms. Martinez’s success, however, is due to the Department of Homeland Security, which claimed the state’s ID law failed to comply with the Real ID Act and would not be accepted in federal buildings or airports starting in 2018.

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