NORRIDGEWOCK, Maine — At the factory here owned by New Balance, the last major athletic shoe brand to manufacture footwear in the United States, even workers on the shop floor recognize that in purely economic terms, the operation doesn’t make sense.

The company could make far more money if, like Nike and Adidas, it shifted virtually all of these jobs to low-wage countries.

So employees try each shift to make it up. Conversations on the shop floor are sparse at best, and the tasks at each work station have been stripped of waste and precisely timed. Workers cut leather for a pair of shoes in 88 seconds, handle precise stitching in 37 seconds, and glue soles to uppers even faster.

“The company already could make more money by going overseas and they know it,” said Scott Boulette, 35, a burly team leader who has his son’s name tattooed in Gothic letters down his left forearm. “So we hustle.”

Now, however, comes what may be an insurmountable challenge. The Obama administration is negotiating a free-trade agreement with Vietnam and seven other countries, and it is unclear whether the plant can stand up to a flood of shoes from that country, already one of the leading exporters of footwear to the United States.

“We are deeply concerned by the inclusion of Vietnam in a potential free-trade agreement,” said Rob DeMartini, president and chief executive of New Balance.

The workers’ predicament highlights the difficulty facing the Obama administration as it seeks free-trade agreements as a potential remedy for U.S. unemployment, now at 9.2 percent.

Backed by many economists, the administration says the agreement with Vietnam and the other countries, the Trans-Pacific Partnership, would create U.S. jobs by opening up Asian countries to U.S. exports such as computers from California and paper products from Maine.

“This agreement will create a potential platform for economic integration across the Asia-Pacific region, a means to advance U.S. economic interests with the fastest-growing economies in the world,” U.S. Trade Representative Ronald Kirk told Congress in announcing that negotiations were about to begin.

Moreover, importing shoes from Vietnam at lower costs would benefit some in the United States, either by reducing prices for consumers or raising profits for manufacturers that have their operations overseas.

But the example of New Balance, which has long resisted the exodus of American footwear manufacturers, highlights the fact that despite the benefits of free trade, it can also destroy some U.S. jobs, and those losses are felt more acutely in a time of high unemployment.

“We want to fight really hard to keep this business in Maine,” said Lori Cook, 28, a single mom with two kids. “I’d like to keep my job.”

The company’s primary concern is that any free-trade agreement with Vietnam would likely eliminate the steep tariff on footwear imported from that country, making Vietnamese sneakers even cheaper than they already are.

New Balance officials said removing the tariff would also undermine years of efforts at the company’s five New England factories to compete against cheap foreign labor. The plants employ 1,000 workers.

Those employees earn upward of $10 an hour, plus benefits, while labor costs in China are about $1.50 an hour, and even less in Vietnam.

With the support of some New England legislators, the company is hoping that an unusual exemption can be created in any agreement with Vietnam to maintain the tariff on the shoes New Balance makes in the United States.

“Making footwear in the U.S. isn’t as easy or as profitable as making them overseas. If it were, every company would still be doing it,” DeMartini said. “We will continue to ask our negotiators to embrace President Obama’s manufacturing agenda and to save what is left of our nation’s once-vibrant shoemaking economy.”

For decades, shoes coming in from China and Vietnam, the largest sources of imported footwear, have been hit with tariffs of as much as 20 percent or more.

The shoe tariff, by pushing up the cost of importing shoes, means a pair of athletic shoes made in the Norridgewock factory or anywhere else in the United States is more competitive than it otherwise would be, and partially offsets the costs of higher wages paid here. On a pair of shoes that comes into the country valued at $30, for example, a typical 20 percent duty amounts to $6. (In many cases, the markup amounts to 100 percent, meaning those shoes would sell to consumers for $72.)

As workers in New England look around at the shuttered textile and shoe mills that still dot many towns, relics of the industrial era, some see the shoe tariff as the least the United States could do for what’s left of the battered industry. In their view, removing the tariff only rewards those companies like Nike and Adidas that have shut U.S. factories and concentrated their operations elsewhere.

Adidas’ last plant was in Kutztown, Pa. Joanne Twomey, 65, worked at the Nike factory in Saco, Maine, until it closed in the mid-’80s, the last significant Nike shoe plant in the United States.

“I have not bought one thing from Nike ever since,” Twomey, now the mayor of nearby Biddeford, Maine, says. “I tell my children and grandchildren not to buy it either. They owed it to the people who got them to the top — the workers in the U.S. — to stay.”

About 25 percent of the shoes New Balance sells in North America are either manufactured or assembled at one of the five New England factories, despite the likelihood that owner Jim Davis could improve profits by joining other shoemakers overseas.

But while the tariff may be protecting New Balance’s 1,000 U.S. workers, it appears to have done little to protect the rest of the U.S. shoe industry, which employed as many as 250,000 people in the ’50s but fewer than 15,000 people today.

“The production of footwear is still very much a labor-intensive process,” said Erin Dobson, Nike spokeswoman. “This, combined with the cost of labor in the U.S., makes it cost-prohibitive based on the way product in our industry is manufactured today.”

She noted that while the company has no shoe manufacturing in the United States, it directly employs 22,000 in the country.

Since about 99 percent of shoes sold in the United States are imported, removal of tariffs likely would save consumers money and help improve profits for retailers and companies that do their manufacturing overseas. Those companies have banded together in recent years to lobby against what they call “the shoe tax.”

“If you are buying shoes, you’re paying a shoe tax,” said Nate Herman of the American Apparel and Footwear Association, which has led the fight against the shoe tariff and supports the Trans-Pacific Partnership. “For products that are no longer produced here and haven’t been produced here for decades, there’s no sense for consumers to be paying it.”

The employees at the factory here shrug off the cost to consumers, and question how it is that a move to save jobs could be considered bad economic policy, as economists often say, when jobs are so hard to come by and they have tried so hard to compete.

Since 2004, the 350 workers at the plant have increased daily production by nearly 9 percent while significantly reducing errors, plant manager Raye Wentworth said. The Maine unemployment rate is nearly 8 percent.

Some like Michelle Witham, 40, count three generations involved with footwear manufacturing. She works at the New Balance factor here, as did her parents. Her grandparents worked in the same building, too, years ago, when it was a shoe factory for another company.

“When I started, people would say, ‘Oh you don’t want to work there. They’re not going to be around for long. They ain’t got a chance,’ ” Witham said. “But I’ve been here 20-something years now.”

“If customers pay a few more dollars for a pair of shoes, then so be it,” said Sheri Fuller, 54, who has worked at the factory for 24 years. “If you take jobs away from people, the hit is going to be a lot bigger.”