When Shawn Fain, the United Automobile Workers president, unveiled the deal that ended six weeks of strikes at Ford Motor in the fall, he framed it as part of a longer campaign. Next, he declared, would be the task of organizing nonunion plants across the country.

“One of our biggest goals coming out of this historic contract victory is to organize like we’ve never organized before,” he said at the time. “When we return to the bargaining table in 2028, it won’t just be with the Big Three. It will be the Big Five or Big Six.”

Four months later, the first test of that strategy has come into focus, and it features a Volkswagen plant in Chattanooga, Tenn.

According to the union, more than half of over 4,000 eligible workers have signed cards indicating support for a union. Workers say they have done so because they want higher pay, more paid time off and more generous health benefits — and because the recent strikes at Ford, General Motors and Stellantis persuaded them that a union can help win these concessions.

“The Big Three, they had their big campaign, and their big strike and vote, and new contracts — we paid attention to that very closely,” said Yolanda Peoples, who has worked at the Volkswagen plant for nearly 13 years.

The Volkswagen plant announced an 11 percent pay increase shortly after the strikes at the Big Three. The raise brought the top hourly wage for production workers to $32.40, but the comparable wage for the Detroit automakers will exceed $40 by the end of the new contracts. (Volkswagen said the wage adjustment was part of a yearly review.)

Unions need a simple majority of votes to win, but the U.A.W. says it won’t file for an election at the Chattanooga plant until 70 percent of the plant’s workers have signed cards and workers have built an extensive organizing committee, which union officials expect in the next month.

The caution reflects the U.A.W.’s experience in the South, where past campaigns fell short.

But the stakes may be even higher this time given the union’s investment in organizing several plants at once — including a Mercedes-Benz factory in Alabama, where more than 50 percent of workers have signed cards, and a Hyundai plant in Alabama, where the union has cards from more than 30 percent of workers.

Last week, the union said it was also allocating $40 million to organizing auto and battery workers through 2026 — far exceeding its previous budget for such efforts, according to Jonah Furman, a union spokesman — and suggested that time was of the essence.

“In the next few years, the electric vehicle battery industry is slated to add tens of thousands of jobs across the country, and new standards are being set as the industry comes online,” the union said in its funding announcement.

If the union wins in Chattanooga, said Joshua Murray, a sociologist at Vanderbilt University who has studied the auto industry’s response to unionization, it may quickly replicate the victory at other plants, as it did during an organizing wave in the 1930s.

“A lot of time the failure to unionize is not that workers are against being in a union — it’s that they’re not convinced they can win,” Dr. Murray said. “Showing they can win is a big deal for getting workers who weren’t gung-ho about it to be gung-ho.”

A loss in Chattanooga, Dr. Murray said, could sap employees’ confidence and encourage management at other automakers to resist.

Other analysts, like Sam Fiorani, vice president of global vehicle forecasting at the research firm AutoForecast Solutions, predicted that Tesla would be a particular challenge. “The head of Tesla is Elon Musk, and he’s going to fight against change,” Mr. Fiorani said.

The union appears to be benefiting from a resurgence of interest in organizing after a lull during the presidency of Donald J. Trump and the start of the pandemic. Last year, unions won more than 1,225 elections — the most in at least a decade, according to the National Labor Relations Board. They lost about 500.

Polling shows that younger workers are especially supportive, and they appear to be helping to fuel the recent auto industry organizing. “We’re letting them know, ‘You’re making a nice pay rate compared to your age, but this can be better,’” said Ronald Terry, a worker involved in the organizing at the Hyundai plant in Alabama.

Younger workers at the Volkswagen plant also express frustration at the paid time off they accrue: 12 or 13 days during their first two years of employment, several of which they must use during plant shutdowns if they want to be paid.

Asked about the complaints, a Volkswagen spokesman said that the company understood that time off was a significant issue and that it had recently announced an increase in unpaid time off for emergencies.

The company said last month that its Chattanooga wages had increased at nearly twice the rate of inflation since 2013, and that the average production worker would make more than $60,000 this year before bonuses or overtime and pay less than $2,000 in premiums to cover more than 80 percent of health care costs.

The union sought a vote in Chattanooga in 2014 and faced no opposition from the company, whose worldwide plants are mostly unionized. But the effort failed amid pressure from state Republican leaders, who suggested that a union would jeopardize the plant’s expansion.

With workers complaining of understaffing, high injury rates and last-minute overtime, the U.A.W. tried again in 2019. But pleas from Tennessee’s governor and the plant’s original chief executive, who said he had returned to his former position to address workers’ concerns, appeared to defuse support. The union narrowly lost.

This time, the union appears determined to minimize the effect of such pushback.

The union wants to recruit a volunteer leader for every line on every shift at the plant — more than 125 altogether, according to the union’s tally. That way, organizers say, the volunteers can quickly respond to rumors or company talking points that co-workers encounter.

“If you don’t have someone continuing that conversation, we have seen some of that backsliding in a few smaller areas,” said Isaac Meadows, a worker involved in the organizing.

He attributed the backsliding to the influence of outside groups and chatter from workers’ friends and relatives that a union would discourage employers from locating in Tennessee.

Gerald McCormick, a Republican who as the state’s House majority leader opposed the union during the 2014 vote, said Republicans might worry that the union would support left-wing causes in Tennessee if it got a foothold there.

“They don’t want to do them any favors,” he said, referring to the state’s Republican leadership, which he predicted would oppose the union campaign again.

As in 2019, the employer’s response may be crucial. The Volkswagen brand appears to be roughly holding its own in the United States, and somewhat ahead in the transition to electric vehicles.

More than 11 percent of Volkswagen’s U.S. sales last year came from E.V.s — specifically the ID.4, a compact sport utility vehicle built in Chattanooga. That figure was higher than the overall 9.4 percent share for plug-in vehicles in the U.S. market, according to BloombergNEF, an energy research firm.

A Volkswagen official said during a tour of the plant that about one-third of its output this year would probably be ID.4s, and that the share could double within a decade.

If that happens, the plant may be relatively well positioned to absorb higher labor costs. Corey Cantor, an electric vehicle analyst at BloombergNEF, said continued battery innovation, along with efficiencies from larger-scale battery production, could offset the cost increases associated with unionization.

But a union presence could complicate the ramp-up in electric vehicle production, Mr. Fiorani of AutoForecast Solutions said, if the union resists the decline in workers per car that may accompany the shift. He noted that companies that made their own batteries might be able to reallocate those workers rather than lay them off, however.

Pablo Di Si, the chief executive of Volkswagen Group of America, said in a statement that the plant had already added jobs in battery pack assembly and battery engineering.

Meeting with reporters last month, a Volkswagen official said that the company would stay neutral during an election campaign, but that “neutral doesn’t mean silent — it means impartial to what employees decide.”

The official added that the company would correct misinformation, which it accuses the union of spreading, about pay and working conditions in the plant. (Companies reaching neutrality agreements with unions typically do not intervene this way.)

Mr. Meadows, the union supporter, said managers had communicated skepticism in sometimes subtle ways, like removing union fliers from lunch tables.

“Somebody put out a couple of business cards for a lawn service company, and we had some material on the same table,” Mr. Meadows recalled. “Our materials disappeared, and the others did not.”

Volkswagen said the cleanliness of the tables was governed by “clear policies.”