Ohio Gov. John Kasich speaks at a GOP Get Out the Vote rally in Independence, Ohio, on Sept. 29. (Mark Duncan/AP)

In an autumn of discomfort for many incumbent governors, Ohio’s John Kasich is smiling. He is coasting toward a second term in a state that long has been one of the nation’s presidential battlegrounds, campaigning on policies he believes can put a more empathetic face on the national Republican Party.

His economic philosophy is Republican orthodoxy, drawn from supply-side theory and coupled with a reformist streak. But what sets Kasich apart from some others in his party is his willingness to use the levers of government and the zeal with which he has embraced his own version of compassionate conservatism, with strong religious overtones.

As the governor of a pivotal Midwestern state, Kasich is seen by some strategists within his party as a potential presidential candidate in 2016. Whatever his intentions or prospects, he is nonetheless eager to put himself into the competition to reshape a national party that has lost the popular vote in five of the last six presidential elections.

“My party is me,” he said in a lengthy interview recently at the Ohio Governor’s Residence. “I have a right to shape my party. I have a right to have an opinion about what my party ought to be. Who’s defining for me what my party is? I’m trying to define what I think the party is.”

Kasich, who defeated Democratic incumbent Ted Strickland in 2010, can look just beyond his borders and see fellow Republican governors struggling in their reelection campaigns. Pennsylvania Gov. Tom Corbett is one of the most endangered incumbents in the nation. Michigan Gov. Rick Snyder and Wisconsin Gov. Scott Walker face stiff competition but could survive.

Kasich is in a far more enviable position, with recent polls showing him with a double-digit lead over his Democratic challenger, Cuyahoga County Executive Ed FitzGerald. Kasich owes his current political standing in part to what he has done as governor. Perhaps more significant is FitzGerald’s late-summer implosion brought on by anemic fundraising, a police report from 2012 that said he had been in a car at 4:30 a.m. with a woman who was not his wife, and the later revelation that he had not had a valid driver’s license for more than a decade.

Kasich won four years ago by just two percentage points. Many recent Ohio gubernatorial elections have not been overly competitive. The high-water mark was set in 1994, when George V. Voinovich was reelected with 72 percent of the vote.

Ohio Democrats have largely given up on the gubernatorial race, but not in their criticism of what they see as the skew in Kasich’s record. “He’s taken all kinds of steps designed to do one thing: weaken the middle class, to exacerbate the problem of income inequality and benefit his rich friends,” said Joe Rugola, director of the Ohio Public School Employee Unit and an international vice president of the American Federation of State, County and Municipal Employees.

But Rugola sees Kasich as a politician with presidential ambitions who doesn’t always fit the mold of other conservatives. “To get there [the presidency], he’s going to have to accommodate far-right funders like the Koch brothers and [Sheldon] Adelson,” Rugola said. “I don’t think he’s abandoned his far-right principles, but I think he’s a smarter politician than a Scott Walker. There’s nothing wind-up, right-wing ideologue about John Kasich. In that regard he’s pretty smart about how he does this.”

If Kasich were to run in 2016, he would probably face some serious obstacles, in part because he has not spent the past year getting ready to run. GOP strategists suggest he would enter as a candidate at the top of the field’s second tier, as neither a purely establishment nor purely tea party candidate. He would carry baggage among conservatives for having expanded Medicaid under the Affordable Care Act but could point to success in Ohio as a sign of how he might do in general-election battlegrounds.

Bragging rights are the domain of every governor, and many can point to economic improvement over the past four years. Kasich is no exception. More than anything, he has focused on what he considers growth-oriented economic and budgetary programs. He closed an $8 billion budgetary hole during his first year in office. He has enacted tax and spending cuts, championed business-friendly regulations, and reformed government programs — all designed to stimulate a state economy long in decline.

Government reforms include steps to slow the growth of Medicaid spending, privatize economic development and calculate aid to colleges and universities based on course completion and graduations rather than simply on enrollment.

He claims significant success in job creation as well. When he took office, the state unemployment rate was 9.1 percent, down from a peak of 10.6 percent in December 2009. The current rate is 5.7 percent — below the national average.

Rankings by the W.P. Carey School of Business at Arizona State University rank Ohio 37th in the nation in total nonfarm jobs created this year. On a regional comparison, Ohio ranks ahead of Pennsylvania, Michigan and Illinois but behind Indiana and Wisconsin on that indicator.

Scott Milburn, Kasich’s communications director, said current-year figures overlook bigger gains in earlier years. Dennis Hoffman, director of the Carey School’s L. William Seidman Research Institute, said Ohio is in “more of an enviable position” when measured by the growth in manufacturing or goods-producing jobs. Ohio ranks 18th in the first and 19th in the second.

John Green, director of the Ray Bliss Institute at the University of Akron, described Kasich as policy-oriented and immersed in the details. His blue-collar roots and religious convictions, Green said, have produced a governing philosophy that merges “sympathy with the welfare state with the idea of smaller government so there will be a higher rate of job growth and economic development.”

The biggest piece of Kasich’s social-welfare agenda was his decision to expand Medicaid under the Affordable Care Act, which he did with a partial end run of the legislature and over objections from conservatives in the state House and Senate. Asked how he came to that decision, Kasich said: “Faith is important to me. If you go through the Old and New testaments, there’s one thing that’s very clear. You’ve got to help people that are downtrodden and poor, and I just think that that’s part of our culture. You’ve got to help people that can’t help themselves.”

Other initiatives aimed at ­lower-income Ohioans — those with addictions or mental illness, at-risk children and others in need — include an earned-income tax credit, a school reform plan for Cleveland, sentencing reform and efforts to tackle human trafficking.

It is difficult to add up the value of the programs he has promoted that might fall under the umbrella of the Kasich social gospel. Those designed specifically to combat drug addiction and treat mental illness have grown 21.6 percent in four years — more in percentage terms than education or higher education. Still, they account for just 1.6 percent of total state spending, according to the Ohio budget office.

Kasich’s policies have brought criticism from both left and right. Dale Butland of Innovation Ohio, a progressive advocacy group, said: “Talk is cheap. What he has actually done to help the poor is actually pretty small.” Meanwhile, Tom Zawistowski, a tea party activist, said, “we feel betrayed” by what Kasich has done on Medicaid and state spending.

By one measure, state spending has increased by 23.9 percent since Kasich took office. But Tim Keen, director of the Ohio Office of Budget and Management, said that number is misleading because it reflects high and distorted growth percentages for Medicaid and debt-service spending. Adjusted for those factors, he said, spending has increased only 12.7 percent.

Yuval Levin, editor of the conservative journal National Affairs and a fellow at the Ethics and Public Policy Center, said by e-mail that while he doesn’t agree with all of Kasich’s policies, “most of what he has done has involved a more coherent combination of conservative ideas about how to solve problems with a broader and wider sense of what problems require attention, than many other Republicans have, particularly when it comes to the challenges facing the poor and the burdens faced by working families.”

In conversation, Kasich spews out current initiatives and ideas for new ones at a rapid pace, often shifting from one thought to another mid-sentence. To some admirers, that reflects his openness to innovation and fresh thinking.

“Kasich has a relentlessly energetic approach to learning and team building,” former House speaker Newt Gingrich, to whom Kasich was a key lieutenant as House Budget Committee chairman in the 1990s, said in an e-mail. Gingrich also noted that Kasich has put together a loyal and experienced senior staff.

Arthur Brooks, president of the American Enterprise Institute, said: “Kasich has a great personality. He’s exuberant. He’s enthusiastic. He just likes to try new things. And he’s really unafraid. He’s a person who appears not to have any fear.”

Kasich’s critics see some of those same characteristics as liabilities. They see the governor as hyper and undisciplined, given to impolitic, off-the-cuff remarks, a politician willing to mow down opponents in his path who isn’t sensitive enough to a personality that often grates on others. “He can be very abrasive, but on the other hand he’s a genuine guy. . . whether you like it or not,” said a Republican admirer who spoke candidly on the condition of anonymity.

Kasich may be no less hard-charging than when he was in the House, but he insists that, after a decade in business with the Wall Street firm Lehman Brothers and four years as governor, he is a different person. “I’m an executive now,” he said. “I have to be a bigger leader, more responsible leader, more careful about how I say things . . . and my faith is significantly greater.”

Although Kasich has gotten much of what he’s sought as governor, he suffered a major defeat in his first year in office that still affects him. It came over a bill that restricted collective bargaining rights for Ohio public employee unions, one that was even more comprehensive than a similar bill that roiled Wisconsin that same year. In November 2011, voters overwhelmingly approved a ballot initiative repealing the measure.

“What I learned from it was people weren’t ready for that, they didn’t want that, and when they spoke, I heard them,” he said. “You get into a big disruption only when you have to. I mean, if you have to, you have to. But you don’t want to be doing that.”

He has no appetite for another such fight with organized labor over right-to-work legislation, like that enacted in neighboring Indiana and Michigan. Asked whether he would sign such a bill, he said the legislature will not pass it. With labor and management working well together, he declared, “There’s no reason even to discuss it. Period.”

Expanding Medicaid or resisting a right-to-work law are not the only areas where Kasich parts company with many conservatives. He has supported the Common Core State Standards for schools. On immigration, he thinks Washington has botched border security but said he remains open to providing a path to legal status or even citizenship to those who are here illegally.

Kasich ran for his party’s 2000 presidential nomination but folded his campaign in July 1999. Now he’s being mentioned again, one of more than a dozen Republicans considered possible candidates. Among them is Sen. Rob Portman of Ohio, who also has a loyal following in the state. Portman served as budget director in the George W. Bush administration, and his low-key personality is a mirror opposite of the governor’s.

Last month, Kasich was asked about a 2016 candidacy during a meeting with the editorial board at the Youngstown Vindicator. “Honestly, I just don’t see it,” he said. “I tried it once. You come with me. You can go with me out to Iowa. You wouldn’t believe it. You’d never go to Iowa again.”

In the interview with The Post, Kasich declined to address a possible candidacy but wanted to set the record straight about his comments to the Youngstown paper — at least about his affection for Iowans. “I blew this one,” he said of the comment. “I like the people of Iowa. . . . I never liked the system they had where you had to pay to park your RV in a parking lot. I wasn’t here to insult the people of Iowa.”

Whatever happens after November, Kasich expects to have a voice and won’t be shy about offering his opinions about the future of his party. “I believe that our party needs to be advancing ideas and not this same old business of hiding in the weeds and throwing rocks at somebody else,” he said. “We sometimes don’t show our heart while we are working with our head. This party needs to offer opportunity in a real way.”

Alice Crites in Washington contributed to this report.