The “bombshell” moment of the whole decade-long Chevrolet Cobalt ignition-failure saga—for which General Motors GM has already set aside $1.1 billion, with far more costs possible—occurred on April 29, 2013, in a conference room at the Detroit airport Westin Hotel. A GM lawyer used the vivid term in an email direct from the room after a victim’s lawyer showed that the Cobalt’s ignition switch had been changed between 2005 and 2008.

It hardly sounds dramatic, but that simple fact, which GM’s own engineers had failed to unearth for years, was the missing piece in the puzzle of what had gone wrong with the Cobalt. It explained why airbags failed to deploy in some crashes, killing at least 13 people, and why those failures stopped after the 2007 model year. Now the company knew exactly where the problem was. And if you want to see the worst symptoms of a deeply dysfunctional corporate culture doing its damage, consider what happened next.

What happened was nothing. No order for an immediate recall, no report to high-level executives. Not even the general counsel was told. Instead, in the words of the damning Valukas report on the affair, which GM commissioned this year, “The response to the revelation…was to hire an expert.” It took six months for the expert to provide his written report, which merely concurred with what outsiders had been telling GM for years: that faulty ignition switches too easily turned from “run” to “accessory” mode, disabling the airbags.

After that, surely, it was time to act. Thousands of consumers were driving cars with a deadly defect that could now be explained. But no, now the engineer in charge of GM’s investigation had to read the report and reach his own conclusion—which turned out to be the same as the expert’s and, for that matter, the same as what a Wisconsin state trooper had concluded six years earlier.

So now was it time for the recall? Not yet. The Valukas report, which repeatedly cites the problems caused by GM’s “proliferation of committees,” says the engineer’s “conclusion was reported to yet further committees.”

Mary BarraWhen she was HR chief, Barra shocked GM lifers by reducing a 10-page dress code to two words: “dress appropriately.”Photo: Ben Baker—Redux

GM finally issued its first Cobalt recall on Feb. 7 of this year, nine months after the puzzle had been solved and, the Valukas report concludes, 2 years after GM knew enough about the problem to justify a recall (and 12 years after the problem first manifested itself). Whether any additional people died as a result of those final months of internal stasis may take years to determine.

But the Cobalt affair makes starkly clear what everyone in the auto industry has known for decades: The GM culture needs to be changed profoundly, and changing it will be one of the titanic struggles in the history of American management.

Mary Barra, still just nine months into her tenure as CEO, is embracing the struggle and means to use the Cobalt mess to her advantage. She accepts that it exposed systemic problems. “I don’t want to set it aside and explain it away,” Barra says, “because I think it uncovered some things in the company that it’s critical we challenge ourselves to change and to fix.”

OUT OF THE ABYSS GM's economic profits. * Earnings adjusted for cost of capitalOUT OF THE ABYSS GM’s economic profits. * Earnings adjusted for cost of capitalGraphic Source: Eva Dimensions

To borrow an old line, she’s not going to let a crisis go to waste. “We didn’t have to work too hard to make the case for change because clearly it was deeply troubling,” Barra says. “Anytime you want to drive change, you have to have a catalyst for change, and it did provide that. I will also tell you it’s made me more impatient.”

Her approach to changing the culture is highly un-GM-like. She hasn’t launched a program or put out a 10-point plan; almost incredibly, she hasn’t formed a committee. Her approach is modest and audacious at the same time: She proposes to alter the mindset by behaving differently every day than any GM CEO has behaved in decades, and through her example and a CEO’s influence, to change the way everyone else behaves every day. As she says, “Culture is how people behave.”

As the Cobalt mess shows, GM has a culture in which people try hard not to bring bad news to higher-ups. It’s been that way for decades. Practically no one is ever accountable for a decision, partly because most decisions are made by committees, and even then the process is a charade because key participants agree privately on the outcome ahead of time. Virtually no one gets fired for performance. Rare threats to the established order can almost always be waited out. Combine those traits, and you get an organism, the GM culture, that is highly evolved for survival. The problem is that it’s hobbling its host.

Is Barra the right person to transform this sprawling, wily beast? You could make a case that she isn’t. She’s the ultimate insider, a second-generation company lifer who was born into the GM way. Her father, a diemaker, worked at the company for 39 years, and she has worked there since age 18, when she enrolled at General Motors Institute to get an engineering degree, later earning a Stanford MBA on a GM fellowship. A culture-changing CEO must act with unchallenged authority, yet she isn’t the board chairman—that’s retired Cummins CEO Tim Solso—and the other contenders for CEO, president Dan Ammann and executive vice president Mark Reuss, both of whom had significant internal support for the top job, are still there.

The stronger case, however, holds that Barra is in fact well-suited to the job. She can hit the ground running because she understands the institution in her bones. She’s only 52, so waiting her out won’t work. Most important, she is already setting an example by violating the norms of the culture. She fired 15 employees in the wake of the Valukas report—a seemingly modest response, but very unlike GM—and she has moved out at least seven high-level executives in her first eight months as CEO, another shock to the system.

The GM playbook says safety problems like the Cobalt matter get patched and dispatched quickly. Barra has done the opposite, telling employees at a town hall meeting, “I never want to put this behind us. I want to put this painful experience permanently in our collective memories.” It was clearly the right message, but was jaw-dropping at GM. Retired executive Steve Harris, who started at GM in 1967, observes, “Her remarks at that meeting were unlike anything any previous GM CEO has ever said.”

Mary Barra“Don’t confuse progress with winning,” says Barra. “I accept no excuses for why we can’t be the best.”Photo: Andrew Harrer—Bloomberg via Getty Images

Barra conveys an unusual personality mix. Many observers have noted her plain, sincere manner. Being genuinely contrite about the Cobalt mess has helped her and GM with senators, victims’ families, and the media. At the same time, a marked steeliness is never far away. Talking about the behaviors she expects from her top team—directness, transparency, candor—she says, “I’m not asking people to do it. It’s a requirement—not only that they hold themselves accountable to do it, but they hold each other accountable. That’s the message I’ve delivered and will continue to drive through the whole organization. This is not optional.”

Still, the worrisome fact is that most of GM’s seven previous CEOs, going back to Roger Smith in the 1980s, tried to change the culture, and the culture won. Is it possible that no one can defeat it? Warren Buffett, who is a major Barra fan and a GM customer (he bought a new Cadillac in July) and whose Berkshire Hathaway recently bought more GM stock, thinks she can succeed where all those others failed. “Mary is as strong as they come,” he says. “She is the person to have there. She is as good as I’ve seen.”

Buffett may well be right, as he so often is. But this is one bear of an assignment. GM’s way of being is the kind that’s hardest to change: embedded in a big, old company that utterly dominated its industry for decades. Cultures like that have occasionally been altered. Jack Welch did it at General Electric GE in the 1980s; Lou Gerstner did it at IBM in the 1990s; Doug Conant did it at Campbell Soup in the 2000s. But more often the transformations fail, as they did at Kodak, Sears, Westinghouse, Pan Am, and many other storied colossi that succumbed largely to their own weaknesses. The odds are against GM, and another factor makes the challenge even harder. Employees have seen it all before. Over the past 30 years they’ve learned that CEOs come and go, but the way we do things around here is invulnerable. At GM, trying and failing to change the culture is part of the culture.

Change is urgent, a reality that many inside and outside the company have overlooked since the company exited bankruptcy in 2009. Although GM is no longer in danger of failing, it isn’t performing nearly well enough and risks fading into long-term weakness. It’s making excellent-quality vehicles, but it has fallen behind competitors in globalizing and improving fuel economy. Since its stock resumed trading in November 2010, the market has rocketed 60%, while GM’s has been flat. Bankruptcy unburdened GM of vast debts, but that has enabled it to earn only its cost of capital (which it hadn’t managed to achieve for decades). As a financial performer, GM has really upped its game and become mediocre. It has a long way to go.

GM SHARES GET LEFT BEHINDGraphic Source: Bloomberg

Barra knows it. “A phrase I use internally a lot is, ‘Don’t confuse progress with winning,’” she says. “It’s one thing to be making continuous improvements and say, ‘This year I got 10% better,’ but if you’re still last, you have to have that external view and know what it’s going to take to become the best.” Which is what she expects GM to do. “I accept no excuses for why we can’t be the best,” Barra says.

Measuring success against external rather than internal standards, fundamental as it seems, represents a major shift in perspective at GM and is a good example of the task Barra faces. GM has long been obsessively inward-looking. “I had a vehicle line executive come to me with his scorecard” in the past decade, recalls former vice chairman Bob Lutz, who has been a top executive at all three Detroit carmakers during his 60-year career. “He said, ‘I’ve completed the most successful program in the history of the vehicle line executive system,’” and he wanted to talk to Lutz about a bonus. His scorecard “had about 50 metrics on it, scored red, yellow, or green, and they were solid green, top to bottom,” the first time that feat had ever been accomplished. “I said, ‘That’s nice. How’s the car selling?’ He said, ‘Oh, it’s not selling at all. The public doesn’t like it.’ I said, ‘You failed! I don’t care how many metrics you got right. You failed!’” The incident illustrates the larger problem—maybe the most serious of GM’s behavioral deficiencies, Lutz believes—that “everything was internal criteria. The idiotic assumption was that if you fulfill all the internal criteria, somehow the car will be a success.”

Another former executive, consultant Rob Kleinbaum, agrees that GM’s insularity may be its worst failing. “Of all GM’s cultural problems, [insularity] might be the most crippling as it perpetuates an inward focus that is largely responsible for its hostile relations with its dealers and suppliers and, most troubling, with consumers,” he wrote in an influential 2009 report, “Retooling GM’s Culture,” which helped guide the presidential task force that managed the GM and Chrysler bailouts. “Much more attention is given to wondering what the senior leadership will think than to figuring out the right path and trying to make it happen.”

Barra’s approach to fixing the problem, unique in GM’s long history of attempted change, is micro-based rather than macro-based. “I kind of hate when we talk about culture,” she says. “What is culture? It’s how people behave. So if we want to change this elusive culture, it’s changing behaviors. And that becomes actionable very quickly. It’s everyone’s behaviors. It’s mine—I have to change my behaviors.” It’s hers especially because the way she interacts with others will cascade through the organization. She realizes that the change will consist of countless individual moments: “It’s every interaction I have with the leadership team. It’s every time I interact with employees, being crystal clear about my expectations. And frankly, you know, that’s somewhat different than maybe General Motors has been in the past.”

She’s being diplomatic. It’s completely unlike GM in two ways. First, few people are ever told that anything in particular is expected of them and that they’re accountable for it—one of the culture’s most damaging elements. Second, previous reform attempts have used the blunderbuss approach rather than focusing on moment-by-moment behavior change. Fixing GM’s stagnation was a major reason Roger Smith spent $2.6 billion in 1984 to buy EDS, Ross Perot’s highly successful software company. “Smith told me he’d tried everything to change the culture, without success, and now these high-performing EDS people would bring their culture to every part of GM,” recalls Ken Langone, the investment banker best known for co-founding Home Depot, who worked on the EDS deal. “Exactly the opposite happened. The GM culture took over EDS. By the time EDS was spun off from GM in 1996, it was bureaucratic and cost-laden.”

Perot famously observed that “the first EDSer to see a snake kills it. At GM, the first thing you do is organize a committee on snakes. Then you bring in a consultant who knows a lot about snakes. Third thing you do is talk about it for a year.”

When GM decided that its dysfunctional culture was a snake under CEO Fritz Henderson in 2009, it followed the script with almost comical precision. First it organized a committee, the culture transformation team. Then it hired a consultant who knew a lot about culture change, from the management consulting firm Booz & Co. It was well on its way to talking about it for a year when the board replaced Henderson as CEO and the project died.

To see the difference in Barra’s approach, consider another GM pathology, the taboo on genuine debate in meetings. A former high executive recalls being new at GM in the early 2000s, when it launched a dramatic remake of Cadillac. “The concept vehicle was absolutely stunning—wow, what Cadillac once was,” he says. But the engineering establishment resisted a complete redesign, instead wanting to build the car off the Corvette platform, “getting fairly close to the vision of the concept car, but not in the way it captured the imagination of the public,” the executive says. At a meeting ostensibly to decide the issue, “there were impassioned presentations by each side, and then it was polite thank-yous, and everybody walked out. No discussion. I was stunned. I asked someone what had just happened. They said it had all been settled beforehand. The old guard had already won. This was just to show that each side had had its say.”

Barra insists that those days are over. “Not that I want to be described as mean, but I think the company’s too nice,” she says. “This is a challenging business, and if you get 16 people in the room like my leadership team and you don’t get all the best thoughts onto the table, you may not be making the right decision. Everybody knows I expect them to get their thoughts on the table. It’s okay to have debates. It shouldn’t be personal or petty or mean. But it can be uncomfortable, because if we have different opinions, we’ve got to talk it through.” Again, the emphasis is not on grand-scale transformation but on changing specific day-to-day behaviors, starting at the top.

In her quest to transform America’s most recalcitrant corporate culture, Barra is taking the right first steps. She’s already ahead of any predecessor’s efforts, and she took some small steps in the right direction in previous jobs. When Barra was made human resources chief in 2009, she found that GM still had a 10-page dress code. When she replaced it with a two-word code—“dress appropriately”—some managers freaked out. They felt they were “in this rules-based organization where I don’t have to think—I just follow these rules,” she recalls. That’s what prompted her to launch new managerial training worldwide, “to reignite the managers.” It’s another sign of how far the company has to go.

Even in the U.S. auto industry, GM is far behind. Chrysler has long had a scrappier temperament than the other two, and Alan Mulally’s turnaround of Ford is already legendary. “Ford is light years ahead culturally,” says Noel Tichy, a University of Michigan management professor who has consulted for GM and Ford in the past. But at least Mulally’s achievement shows that “it can be done in that industry.”

The best reason to be optimistic about Barra’s chances is that, just as she isn’t attempting the change in the old-GM way, she isn’t measuring success that way either. How will she know whether she is actually changing the culture? “The ultimate proof point will be when we deliver exceptional financial results by continuing to do exceptional products and providing an exceptional customer experience,” she says. That is, she’ll look outward. Very un-GM-like. “That’s how I’ll know.”

This story is from the October 6, 2014 issue of Fortune.