The justices are considering the constitutionality of a New York law that makes it hard for residents to obtain a permit to carry concealed firearms in public. The court, with three conservative pro-gun justices appointed by former President Donald Trump, will almost certainly say New York’s law is too restrictive under the Second Amendment — which will lead, predictably, to more guns on city streets and more violent crime.

The New York case could also signal the beginning of a new era of judicial hostility to gun laws, especially to the bans on assault weapons and large-capacity magazines that the reinvigorated gun safety movement has fought so hard to get enacted. With a single decision, the Supreme Court majority could transform life in many American cities — and stymie the growing political movement for gun reform.

While the Bureau of Alcohol, Tobacco, Firearms and Explosives, or A.T.F., has federal gun law enforcement authority, the National Rifle Association and its allies have shackled it with outdated technology, insufficient funds, and absurd restrictions. With an ever-increasing number of guns in the United States, A.T.F.’s intentional impotence comes at a deadly cost.

Now the long-suffering A.T.F. (somehow the “explosives” never made it into the abbreviation) is at the center of President Biden’s plans to push back at what he has called “the international embarrassment” of gun violence in America.

As he laid out his expansive vision for the nation on Wednesday night, Mr. Biden once again called on Congress to expand background checks and ban assault weapons. But given the abiding power of the gun lobby, his immediate hopes lie in a more limited list of executive actions that will ultimately rely on the effectiveness of the A.T.F., the federal agency tasked with enforcing the country’s gun laws and executive actions.

Mr. Biden has ordered a ban on the homemade-firearm kits known as “ghost guns,” a prohibition the A.T.F. will have to enforce. To help set gun policy, he has charged the A.T.F. with undertaking the first comprehensive federal survey of weapons-trafficking patterns since 2000. And to lead the bureau into the future, Mr. Biden has nominated a fiery former A.T.F. agent and gun-control activist, David Chipman.

First, though, the bureau will have to overcome its past. In the 48 years since its mission shifted primarily to firearms enforcement, it has been weakened by relentless assaults from the N.R.A. that have, in the view of many, made the A.T.F. appear to be an agency engineered to fail.

At the N.R.A.’s instigation, Congress has limited the bureau’s budget. It has imposed crippling restrictions on the collection and use of gun-ownership data, including a ban on requiring basic inventories of weapons from gun dealers. It has limited unannounced inspections of gun dealers. Fifteen years ago, the N.R.A. successfully lobbied to make the director’s appointment subject to Senate confirmation — and has subsequently helped block all but one nominee from taking office.

“A.T.F. has all this potential, and they do a lot of good things, but it’s time somebody asked, ‘What is it going to take for us to succeed rather than just treading water?’” said Thomas Brandon, who served as the bureau’s interim director from 2015 until retiring in 2019.

In the weeks after a series of mass shootings prompted calls for action, The New York Times interviewed two dozen people who had either run the A.T.F. or tracked its decline. Their consensus was that the agency needed to be restructured, modernized, given adequate resources and managed in a more proactive and aggressive way.

“What’s been done to the A.T.F. is systemic, it’s intentional and it’s a huge problem,” said T. Christian Heyne, vice president of policy at Brady, a gun control advocacy group that has proposed a plan for executive action centered on enforcement by the agency.

The A.T.F. has also been hindered from within. The bureau’s culture, several people said, prioritizes high-visibility operations, like responding to episodes of violence at the racial-justice protests across the country last summer, over its more mundane core mission of inspecting and licensing gun dealers. That mission took a major step back in 2020 during the coronavirus pandemic, when annual inspections nose-dived by more than 50 percent even as gun sales surged to record levels.

To say the A.T.F. is outgunned is an understatement. Staffing levels have remained essentially flat for two decades, with the number of inspectors who are responsible for overseeing gun dealers actually decreasing by about 20 percent since 2001. The number of firearms sold over the same period has skyrocketed: over 23 million guns in 2020, shattering the previous record of 15.7 million in 2016.

“The A.T.F. is the only federal organization that is basically the same size it was in 1972,” said Dale Armstrong, a retired 28-year veteran of the agency who ran its national gun-trafficking unit.

A Decades-Old Rift

The trouble between the gun-rights movement and the A.T.F. began at least a half-century ago, when armed agents used a battering ram to knock down the door of an apartment in Silver Spring, Md. There had been a report that the resident, a gun collector named Kenyon Ballew, had been seen with several hand grenades.

Mr. Ballew was naked and carrying an antique long-barreled Colt revolver when A.T.F. agents, along with local police officers, crashed through his door. They fired eight bullets, including one that lodged in his brain that left him partially paralyzed.

Mr. Ballew’s case helped instigate a decades-long campaign by the gun lobby and its allies in Congress to undermine the agency.

In 1981, the new president, Ronald Reagan, a staunch N.R.A. ally, announced a plan to abolish the A.T.F. as a stand-alone agency and fold it into the Secret Service. But Mr. Reagan ultimately abandoned the plan at the urging of the N.R.A., which feared that the Secret Service would be a far less appealing foil.

“They’ve always loved to have an agency on the edge that is a whipping boy,” Richard Feldman, a former N.R.A. lobbyist, said in an interview.

The bureau only grew as an object of loathing among many gun owners. In 1993, its agents raided the Branch Davidian compound in Waco, Texas, in an ill-prepared operation against a religious sect that had been stockpiling weapons. Four agents and six sect members died, and a long siege followed, ending with an F.B.I.-led assault weeks later that left more than 70 dead. The A.T.F.’s image never fully recovered.

Timothy McVeigh was spotted by an undercover detective selling baseball caps that had an image of the letters “A.T.F.” speckled with bullet holes two years before he bombed a federal building in Oklahoma City in 1995, killing 168 people.

Soon afterward, the N.R.A. put out a fund-raising letter that referred to the A.T.F. and other federal agents as “jackbooted government thugs.”

In response, former President George H.W. Bush resigned as a member of the group in protest, and even Wayne LaPierre, who has led the N.R.A. for three decades, conceded in a 2019 interview with The Times that the letter had gone too far.

While he might regret the rhetoric, Mr. LaPierre nonetheless pursued a legislative strategy that eroded the A.T.F.’s authority.

In 2003, the N.R.A. helped draft the so-called Tiahrt amendment — named for its sponsor, former Representative Todd Tiahrt, Republican of Kansas — which put severe restrictions on the A.T.F.’s ability to share gun-tracing data. It also requires the F.B.I. to destroy most gun purchase records within 24 hours after a background check, and it blocks the A.T.F. from requiring dealers to provide records of their inventories.

The onslaught continued. In a series of moves that the N.R.A. backed in 2011, the A.T.F. was barred from transferring enforcement authority to the F.B.I. or the Secret Service, and limits were put in place on unannounced inspections of gun dealers and on digitizing the agency’s records.

The agency was also barred from curtailing imports of shotguns with features that the A.T.F. deemed questionable for widespread use.

Although only a small percentage of weapons dealers are corrupt, the bad actors do a lot of damage — with 1.2 percent of gun dealers responsible for over 57 percent of the guns later traced to crimes, according to bureau estimates.

Some gun shops, the ones deemed at lowest risk for illegal activity, are often not inspected for seven or eight years. Some can go without an inspection for a decade. Locations in “source” areas, places known to be the origin of trafficked guns, are often inspected more frequently, at least once every two or three years.

Even in a good year, the inspections cover fewer than 15 percent of licensed dealers, and the lack of consistent oversight has real-world consequences. A 2009 report by the Congressional Research Service found that “a substantial percentage of recovered firearms cannot be successfully traced for several reasons including poor record-keeping.”

The last major review of the program, conducted by the bureau’s inspector general in 2013, found that only 58 percent of dealers were inspected within the agency’s own five-year time frame, and that officials often “did not track” the actions of high-risk dealers.

Over the past year, A.T.F.’s inspection program virtually evaporated. Inspections plummeted from around 13,000 for the 2019 fiscal year to only 5,827 in 2020. Bureau officials attributed the drop-off to the coronavirus pandemic, which shut some sellers down for months, and the diversion of some personnel to counseling stores on protecting their inventory during the health crisis and the civil unrest.

Critics say those explanations are inadequate, given the huge spike in gun sales last year.

But the A.T.F.’s kid-brother status has often made it difficult to compete for the attention of federal prosecutors who view all but the splashiest gun cases as a time-wasting headache, according to current and former agents.

Here, too, is a dilemma with its origins in the gun lobby’s success in erecting hurdles into law: To convict a dealer of a criminal violation, prosecutors must prove the dealer “willfully” intended to sell weapons for a criminal purpose, a high legal bar.

A Demand for Leadership

The mere presence of a permanent leader, like Mr. Chipman, has the potential to be transformative, former agency officials said.

“I was never the president’s guy, and being the president’s person means people are less likely to push back against you,” said Mr. Brandon, the former interim director. “It gives you a lot more street cred.”

Mr. Chipman served as a special agent during a 22-year A.T.F. career that ended in 2010, first in the bureau’s hectic Detroit office, then in stints working the Interstate 95 corridor, the country’s biggest conduit for illegal firearms, and at bureau headquarters. There, he told the website The Trace, he observed “the catastrophic downsides of the gun lobby efforts to block the A.T.F. from modernizing.”

Needy Road

The Martinsburg center, a nondescript single-story former I.R.S. server farm on a thoroughfare known, appropriately enough, as Needy Road, is just a 90-minute drive north of Washington. But the political machinations consuming the capital are a distant echo here, subsumed by the demands of the job.

The recent rise in gun violence across the country has prompted an uptick in tracing cases: The center had its busiest month in history in March, with 49,000 requests, and A.T.F. officials estimate it will complete 548,000 traces this year — although they have received funding to handle only 375,000, according to a bureau spokeswoman, April Langwell.

“We’re getting a lot more tracing requests, but there’s been no change in our budget,” said Mr. Arnold, who runs the division. “We can handle the most urgent cases in four or five hours. But our average completion times — they are starting to creep up.”

The soft-spoken Mr. Arnold, who has worked in Martinsburg since 2008, prefers to emphasize the positive, praising the skills of the 21 federal gun tracers who stitch together the fragmented histories of firearms, cross-indexing paper records with digitized documents containing serial numbers, points of purchase, names and addresses.

They are supported by contract workers who do the numbing work of retrieving and archiving the old records, flexing their overworked wrists as they thumb through sheafs of yellowed paper. A huge bottle of hand lotion sits at the center of the main room.

The paper records, which must be fed by hand into scanning machines to be stored as visual images, represent three distinct layers of dysfunction: the lack of a modern online filing portal, the prohibition against allowing records to be input as searchable data — so they would not have to be scanned like old family photos — and the failure of Congress to fund enough people to process the information as quickly as it comes in.

The rotating pool of 200 contract workers who unpack the boxes never quite know what they will find when they pop a lid. Sometimes, store owners urinate on documents in protest. It is not uncommon to find guns stashed by dealers in the files, or cash, or, in one memorable instance, an old hand grenade. It turned out to be a dud.

The tracers shrug it all off, and the challenges have cemented their status within the A.T.F. as an elite unit with an uncanny capacity to reconstruct ownership records, sometimes in minutes, in the case of many mass shootings.

It is telling that among the only significant improvements to the process in recent years came not from Washington, but from big-box sporting-good shops that have worked with the bureau to make it easier to file their forms online.

But the digitization, purely voluntary, barely made a dent in the daily shipments of boxes. And none of the new filings can be stored in searchable form — just like the paper ones.