Even before the pandemic, Elsa Rodriguez Killion realized that Casa Corona, her restaurant in Fresno, Calif., was going to have to change with the times.

She spent money on digital marketing. She invested in technology that enabled online orders, for dishes like the restaurant’s signature chile verde. And there was something else she had to keep up with: California’s rising minimum wage.

The minimum rose to $14 an hour on Jan. 1, the fifth annual increase under a 2016 law. It is set to reach $15 for most employers by next year. With price increases, Ms. Rodriguez Killion was able to absorb some of the added payroll expense. But she also cut more than 20 percent of the 160 jobs at her restaurant’s two locations in the last five years, not including those lost because of the pandemic.

“Every year we have had to make hard decisions to let labor go,” said Ms. Rodriguez Killion, 47, who opened Casa Corona with her brother and sister more than 20 years ago. She worries that paring more of her work force is inevitable.

On the flip side of her anxiety is the measurable difference felt by some Fresno workers, even if the higher pay is still often not enough to live comfortably.

“It helps tremendously,” said Elisabeth Parra, 25, a Walmart cashier who lives with her mother. Since her pay rose to the $14 minimum last month, she said, “I’m able to help my mom more with bills.”

Fresno may be a laboratory for a debate that is heating up on the national level. President Biden wants to gradually raise the federal minimum wage to $15 an hour, from the current $7.25, achieving a longstanding priority of the labor movement and the Democratic Party’s progressive wing.

For now, at least, such a provision is part of Mr. Biden’s $1.9 trillion pandemic relief package. House Democrats, who voted in 2019 for a $15 minimum wage, intend to do so again when they send the pandemic legislation to the Senate. But chances there are clouded by parliamentary questions — and the objections of two key Democrats, Joe Manchin of West Virginia and Kyrsten Sinema of Arizona, along with Republicans.

Backers have long said that increasing the minimum wage would raise the living standard of workers and help combat poverty. With more money, workers would be inclined to spend more, strengthening the economy.

Opponents contend that minimum-wage increases cost jobs, particularly in struggling cities like Fresno. What’s more, they say, any broad standard, whether statewide or nationwide, does not account for local variations in the cost of living or business conditions.

According to a study by the Congressional Budget Office, raising the minimum wage to $15 by 2025 would decrease employment by 1.4 million — but it would still raise 900,000 people out of poverty. The report’s conclusions were wielded by both proponents and foes of the $15 proposal.

The pandemic-induced downturn has raised the stakes. Those favoring a minimum-wage increase say it is more essential than ever, especially since sectors hit hardest by the pandemic, including leisure and hospitality, have a higher proportion of low-wage workers. Critics counter that lifting the wage floor would severely harm small businesses trying to bounce back.

“This is the debate that usually takes place in some academic circles,” said Antonio Avalos, the chairman of the economics department at California State University, Fresno. But the experience of Fresno, an inland city of 500,000 isolated geographically and economically from coastal metropolises like San Francisco and Los Angeles, underscores the core tension between the competing economic arguments.

Fresno is the hub of an agriculture-rich area, with produce that includes almonds, pistachios, oranges and grapes. Its economy is tied directly to the agriculture industry, though its location has also made it a draw for warehouses. In recent years, Amazon and the beauty emporium Ulta Beauty both opened sprawling fulfillment centers there.

Fresno County, where more than half of the population identifies as Hispanic, has one of the state’s highest poverty rates, and one of its lowest median wages. The typical local worker in 2019, the last year for which data is available, made under $17 an hour. A quarter of workers made $12.50.

Before California enacted gradual increases under its 2016 law, the minimum wage was $10, a level typical for fast-food jobs and other low-wage occupations.

Some Fresno business owners saw little impact from the raises.

Arthur Moye, who owns Full Circle Brewing Company, a craft brewery, has not had to reduce his staff because the wage increases had been “a slow roll,” he said. Instead, he has adjusted both the pay and the work. “We might increase expectations on the people that are here earning that higher wage,” devoting more scrutiny to job candidates and doing more to develop those they hire, he said.

But others, especially restaurant owners like Ms. Rodriguez Killion, say costs are becoming untenable, especially as they contend with the pandemic’s impact.

A 2019 study by the University of California, Riverside, funded by the California Restaurant Association, a trade group, found evidence that the rising minimum wage was slowing growth in the state’s restaurant industry.

Kris Stuebner, an executive at Jem Restaurant Management Corporation, which operates KFC and Wendy’s franchises in Fresno, said the wage mandate had been particularly tough for restaurant operators like him, who have to allocate a percentage of their profits to things like franchise royalties and advertising fees.

He has not reduced his work force, he said. But to offset the rising labor costs, he said, he has had to raise prices and look for places to save money. He formed an internal maintenance department because he could no longer afford to pay an outside company to fix issues like plumbing.

“It’s this balancing act — you’ve got all these balls in the air to juggle,” he said.

Several employers questioned the logic of applying a statewide minimum wage in a place like Fresno, where the cost of living is much lower than in coastal cities. In voices tinged with resentment, some describe the rising minimum wage as akin to a “payroll tax grab” by the government because payroll taxes for employers are tied to employees’ wages and rise when wages do.

Some business owners also noted that they had had to raise wages for employees already making more than the minimum to keep the pay scale fair. And some mentioned indirect results: When the minimum wage increases, the price of other things, from gas to cleaning linens to produce, increases as well.

Yet hiring has continued. According to the Bureau of Labor Statistics, restaurant employment in Fresno rose by about 7 percent from the end of 2016 to the end of 2019, before the pandemic — a slightly higher rate than in California as a whole.

The minimum-wage law allows the governor to delay a planned increase for a year if the economy weakens. With the pandemic gutting their industry, restaurant owners in Fresno and elsewhere urged Gov. Gavin Newsom to do so.

When he didn’t, some owners were outraged.

“It’s frustrating as can be,” said Chuck Van Fleet, the owner of Vino Grille & Spirits and the president of the Fresno chapter of the California Restaurant Association. “You’ve got somebody who’s out there saying, ‘Hey, I’m trying to do what’s right for everybody.’ And the only thing he wants to do is increase wages.”

At the same time, the wage increases in California have offered hope to some workers in Fresno, whose incomes have grown.

Ms. Parra, the Walmart cashier, has lived almost her whole life in Fresno. She recently graduated from California State University, Fresno, with a degree in mass communications and journalism, focusing on advertising, and dreams of becoming an art director.

She was making $15 an hour in a part-time job at a public relations firm before she was let go in the spring during the first coronavirus surge. She started working at Walmart in October for $13 an hour, the minimum wage last year.

When the wage went up, Ms. Parra said, she could more easily help with rent and pay the phone and cable bills at the apartment that she shares with her mother, who makes $18.50 an hour at a heating and air-conditioning company.

She noted, however, that her wages were not enough for her to live on her own. “I wouldn’t say that we’re poor, but I also wouldn’t say that we’re well off,” she said. “But because there is both of us who have incomes, we’re able to do O.K.”

Mayor Jerry Dyer said there were “mixed feelings, obviously,” about the rising minimum wage. “As a mayor of a city, it’s important that we have people in our community who are making a livable wage,” he said.

But Mr. Dyer, a Republican, said he also understood the pain that businesses might be feeling. “I’ve heard from businesses that if the minimum wage goes up too much, they’re not able to be competitive,” he said.

“That’s the challenge that we face,” he said.

One prevailing question is whether $15 is enough.

In Fresno, it often isn’t. M.I.T.’s Living Wage Calculator estimates that a living wage in Fresno for a family of four, with both adults working, is $22.52 an hour. In the past year, Fresno’s median rent increased by 11 percent, to $1,260, according to Apartment List’s National Rent Report, among the greatest increases in the country.

For 40 hours a week, Jessica Ramirez, 26, makes $15.65 an hour at the Amazon warehouse in Fresno. She is the primary breadwinner for herself, her partner and her five children, but even with food stamps and occasional gig work, she said, her wage is barely enough for them to get by.

Ms. Ramirezsaid she was renting a three-bedroom house for $1,350 a month — roughly half of what she makes.

She wants to go to college, but even more, she wants a better life for her children. “I’m their provider,” she said. “I have to give them a home. That’s what they need — a home.”