On a blustery fall morning in southern New Jersey, the weather was too rough for the fishing boats at the center of a momentous Supreme Court case to set out to sea.

A herring fisherman named Bill Bright talked about the case, which will be argued on Wednesday and could both lift what he said was an onerous fishing regulation and wipe out the most important precedent on the power of executive agencies, a long-sought goal of the conservative legal movement.

As workers cleaned squid and the salt air whipped over the docks, Mr. Bright, who has been fishing for 40 years and whose family-owned company is one of the plaintiffs, said he recognized the impact the case could have.

“I can see why this case is such a political thing,” he said. “But to me, it’s not political. This is my livelihood.”

Mr. Bright is backed by a conservative group with ambitions that extend far beyond fishing regulations. Its aim is to do away with a seminal 1984 decision, Chevron v. Natural Resources Defense Council, one of the most cited cases in American law.

The conservative legal movement and business groups have long objected to the ruling, partly based on a general hostility to government regulation and partly based on the belief, grounded in the separation of powers, that agencies should have only the power that Congress has explicitly given to them.

Overturning the decision could threaten regulations on the environment, health care, consumer safety, nuclear energy, government benefit programs and guns. It would also shift power from agencies to judges.

Mr. Bright laid out the basic question in his case.

A 1976 federal law requires herring boats to carry federal observers to collect data needed to prevent overfishing. That was fine with him.

“There’s nothing wrong with the monitors,” he said. “They’re actually gathering information that is valuable to us.”

But a 2020 regulation interpreting the law that required his company to pay for the oversight, at a rate of some $700 a day, was another matter. “I don’t think it’s fair,” he said, adding that Congress had not authorized the agency to impose the fee.

He did the math. In a good week at sea, he said, “we might catch $100,000 worth of herring, which would make us happy.” The monitor’s fee would add up to 5 percent of that, about the same as the $5,000 shares claimed by each of the crew’s four members, who can spend weeks without pay preparing for a voyage. He added that not every week at sea is a good week.

“That tax,” he said, referring to the monitor’s fee, “is going to be very burdensome to a business that’s very burdened in the beginning with all the high fuel costs, all of our supplies, our nets, our gear.”

Mr. Bright did not dispute that Congress may impose such a fee. But he said — and this is the central issue in the case before the Supreme Court — that judges rather than regulators must decide whether the 1976 law allows it.

The Chevron decision established the framework under attack in Mr. Bright’s case, ruling that courts must defer to agencies’ reasonable interpretations of ambiguous statutes.

That statement may seem dry, but it has dictated the outcomes in countless disputes, including Mr. Bright’s case, Loper Bright Enterprises v. Raimondo, No. 22-452, and an almost identical one involving herring fishermen from Rhode Island, Relentless v. Department of Commerce, No. 22-1219, that will be argued alongside it.

In both cases, appeals courts — one in Washington, the other in Boston — ruled that the deference called for by the Chevron decision required a ruling for the government. The United States Court of Appeals for the District of Columbia Circuit, in Washington, ruled that the agency’s interpretation of the 1976 law “to allow industry-funded monitoring was reasonable.” The First Circuit, in Boston, said that “at the very least” the agency’s interpretation of the 1976 law was “certainly reasonable.”

Justice Ketanji Brown Jackson is recused from the first case because she had participated in it as a federal appeals court judge. The Supreme Court agreed to hear the second case in October, five months after it agreed to hear the one from New Jersey.

If the Supreme Court is to overturn a major precedent, the justices apparently calculated, it would be better for the decision to come from a nine-member court.

The cases are in one respect curious, as the Biden administration explained in a brief defending Chevron. “In practice, the 2020 rule’s monitoring provisions have had no financial impact on regulated vessels,” the brief said, adding that the program was suspended last year and the agency reimbursed the monitoring costs that had been incurred under it.

Mr. Bright’s company is represented by Cause of Action Institute, which says its mission is “to limit the power of the administrative state.” The plaintiffs in the Rhode Island case are represented by the New Civil Liberties Alliance, which says it aims “to protect constitutional freedoms from violations from the administrative state.” Both groups have financial ties to the network of foundations and advocacy organization funded by Charles Koch, a billionaire who has long supported conservative and libertarian causes.

In their briefs, the two groups pointed out that Chevron has fallen out of favor at the Supreme Court in recent years, and several justices have criticized it.

Justice Clarence Thomas, in a concurring opinion in 2015, wrote that Chevron “wrests from courts the ultimate interpretive authority to say what the law is, and hands it over to the executive.”

Justice Neil M. Gorsuch echoed the point in a 2022 dissent. “Rather than say what the law is,” he wrote, “we tell those who come before us to go ask a bureaucrat.”

The Supreme Court, which had invoked Chevron at least 70 times to decide cases, has not done so since 2016.

“The question is less whether this court should overrule Chevron,” Paul D. Clement, one of Mr. Bright’s lawyers, told the justices, “and more whether it should let lower courts and citizens in on the news.”

Even as it has ignored Chevron, the Supreme Court has increasingly relied instead on the “major questions doctrine,” which requires Congress to speak particularly clearly when it authorizes the executive branch to take on matters of political or economic significance.

Forty years ago, when Chevron was decided by a unanimous but short-handed six-member Supreme Court, with three justices recused, it was generally viewed as a victory for conservatives. In response to a challenge from environmental groups, the justices sustained a Reagan-era interpretation of the Clean Air Act that loosened regulation of emissions, saying the Environmental Protection Agency’s reading of the statute was “a reasonable construction” that was “entitled to deference.”

The modern conservative attack on Chevron, its supporters say, is an attack on regulation and on the expertise and independence of administrative agencies.

Mr. Clement countered that the question in Mr. Bright’s case and similar ones do not require specialized knowledge.

“Chevron is not limited to thorny technical and scientific questions, as this case well illustrates,” he wrote. “No scientific or technical expertise is needed to determine whether a cash-strapped agency has legal authority to expand its enforcement regime by forcing the governed to foot the bill.”

The challengers in the case from Rhode Island added that expertise does not confer the power to interpret statutes. “No one thinks Congress could force courts to defer to the U.S. Chamber of Commerce in business cases, or to the N.A.A.C.P. in race-discrimination cases, or to the American Medical Association in public-health cases,” their brief said, “simply because these groups have expertise in each subject area.”

The brief raised another objection, saying that Chevron systematically favors the government and so violates due process.

The Biden administration, represented by Solicitor General Elizabeth B. Prelogar, defended the decision, adding that executive agencies, unlike courts, are politically accountable.

“The executive branch,” she wrote, “is controlled by the president, who is chosen by the American people. When a court applies Chevron, it is giving effect to choices the American people made as an exercise of self-government.”

The Supreme Court has in recent years discarded major precedents, notably ones on the constitutional right to abortion and the permissibility of race-conscious admissions in higher education. Ms. Prelogar urged the court to retain Chevron, calling it “a cornerstone of administrative law.”

“Overruling Chevron would be a convulsive shock to the legal system,” Ms. Prelogar wrote.

In Cape May, Mr. Bright said he recognized the impact his case could have.

“The role of government has been a good thing overall, because we know without that most of us would not be fishing today,” he said. But he added that there must be limits.

“I don’t want to do away with the observer program,” he said. “I would just like to maintain what we’re doing without the additional cost.”

Hiroko Tabuchi contributed reporting.