WILMINGTON, Ohio—Gov. John Kasich on Tuesday used a small southwestern Ohio town to show that Ohioans have gotten back on their feet after having the rug pulled out from under them.

Mr. Kasich’s address, which doubled as a commercial for his latest budget proposals, also held up Ohio as an example for an audience well beyond the state’s borders. These days Mr. Kasich’s speeches are watched closely for any hint of a presidential run in 2016.

Mr. Kasich tried to tell Ohio’s story through the eyes of Wilmington. The city along I-71, about halfway between Columbus and Cincinnati, became the poster child for what the Republican said had gone wrong with Ohio’s economy before he took office and what has gone right since.

“I came here to Wilmington during my campaign in 2010, and I saw the devastation this town had suffered,” he said. “It was written on the faces of the people in Wilmington, and these are people who played by the rules. led. They didn't do anything wrong. It reminds me of stories across the country, including my own hometown...The one day the rug was pulled out from under them.”

Wilmington went into an economic tailspin in 2009 when DHL Express moved its local air freight hub, putting about 8,000 out of work. The city has not fully recovered from the wounds of the recession, but neither has Ohio. But Mr. Kasich argued that Wilmington’s story of resilience is one from which Ohio and the nation as a whole can learn.

“The state of the state is getting stronger, and we have regained our footing, but we must act decisively to seize the greater opportunities before all of us...,” Mr. Kasich said. “Wilmington is in many ways a reflection of Ohio We are doing better.”

Cabinet members and legislative committees touted the city’s resilience with its seasonally unadjusted unemployment rate now at 5.8 percent, down from a high above 19 percent five years ago. The current rate is still a full point above the state’s seasonally unadjusted rate of 4.7 percent in December but roughly on par with the national rate of 5.7 percent.

Mr. Kasich has touted the 285,000 jobs created during his tenure as the state continues to work to recover all of the jobs lost during the recession.

John McCarthy, state Medicaid director, touted local examples of those who’ve benefited from the governor’s controversial decision to partner with the federal government to expand eligibility for working adults, extending health coverage to some 450,000 more statewide.

The governor’s budget, which presumes continued funding for the expansion, is now before the same Republican-controlled General Assembly that balked at expansion two years ago.

As he did in his second term inaugural speech earlier this year, he urged the lawmakers in front of him to resist the calls of special interests who will fight some of his proposals, most notably his tax reform plan. Mr. Kasich promises a net cut of $523 million over two years. He has proposed eliminating income tax on the first $2 million in small business earnings and a 23 percent income cut across all brackets for individuals.

To help offset the lost revenue, he has proposed raising taxes in sales, tobacco, oil and gas drillers, and larger business income.

In the past, the Republican-controlled General Assembly has been willing to give him most of what he’s wanted on the cut side of the equation but not nearly as much on the hike side.

Democrats accused Mr. Kasich of doubling down on policies that have not fueled a promised comeback.

“Ohio’s recovery is lagging other states because wages remain stagnant, too many working families continue to struggle, and Governor Kasich keeps asking those with the least to pay more in order to fund tax cuts for those doing well,” state Democratic Chairman David Pepper said in a statement released before the speech.

“The latest budget proposal is more of the same,” he said. “In Wilmington, the average family will have their taxes raised by $122 in the governor’s latest tax plan.”

This marked Mr. Kasich's fifth State of the State Address and the fourth held on the road following Steubenville, Lima, and Medina. This year's speech was held in the home county of new House Speaker Cliff Rosenberger (R., Clarksville).

First Published February 25, 2015, 12:49 a.m.