Can Coda’s electric car survive?

That’s what the star-studded backers of Coda Automotive learned, a roster that includes three former Goldman Sachs (GS) bankers, a founder of the software giant SAP (SAP), the private equity firms Farallon Capital and KKR (KKR), and an ex-CEO of British Petroleum (BP).

This past spring the privately held Los Angeles company launched its $37,250 five-passenger, all-electric sedan. (After federal and California rebates: $27,250.) Its performance is impressive. The Coda can travel as far as 125 miles on a charge — farther than its competitors the Nissan Leaf, Ford Focus, and Mitsubishi i-MiEV. That’s certainly good. But there are a few problems. The company has scant revenues, has no profits, is about two years behind its original production schedule, and is working through its third CEO. So far Coda has sold fewer than 500 cars, whose design looks like a Chinese version of a 1990s Ford Escort.

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Coda’s challenges say a lot about today’s U.S. electric-car industry. Two years ago analysts and many auto executives expected electric-car sales to burn rubber. Now many of those same analysts are saying the market is flat on its back. The truth seems to be somewhere in between. According to Pike Research, this year only about 20,000 all-electric cars will be sold in the U.S.; that number should rise to 28,000 next year. “The market for electric cars is sputtering,” says Michael Lew, an analyst at Needham & Co., “but the price of the technology is falling, and sales will ramp up at some point.”

Other electric-car makers have been struggling as well. Tesla (TSLA), the only other independent all-electric car maker besides Coda, just launched its elegant, technologically sophisticated $57,000 S sedan. CEO Elon Musk, one of the founders of PayPal and the founder of SpaceX, the space transport company, said ominously at a recent appearance at the National Clean Energy Summit that the next six months will determine whether Tesla will survive. Fisker, which sells the Karma, a $103,000 electric hybrid, is trying to produce a less expensive sedan called the Atlantic in a Delaware factory. The company is scrambling to replace a portion of a $529 million federal loan guarantee that was frozen after the company fell behind schedule.

The obstacles that these car makers face are not just technological. With U.S. gasoline prices low by European and Asian standards, and Congress threatening to take away federal subsidies for electric cars and batteries, the American market is becoming less attractive for manufacturers. Also, the rollout of public charging stations is taking longer than predicted. Car buyers, wary of high prices for electric cars, the longevity of their expensive batteries, and the possibility of becoming stranded on a dark highway, have not shown up in droves.

The question is, then: Can Coda and all the other independent electric-car makers scale up production and sales fast enough to avoid becoming yet another casualty in the rough-and-tumble global auto business?

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When Coda was launched in 2009, the future for electric cars looked bright. Kevin Czinger, an ex-Goldman banker, believed the world was going electric. He wanted to be at the forefront of the revolution and joined up with Miles Rubin, a former CEO of Detroit Iron and Steel who later ran Polo Ralph Lauren Jeanswear. Their goal: Build an electric car for the masses. Rubin had already started a company that made low-speed electric trucks called Miles EV. They spun off a company named Coda, the musical term for the end of a piece of music, which meant to suggest that the age of fossil-fuel dependency was over.

Czinger then gathered some of the best engineering minds in the country — he brought in Ken Baker, who ran GM’s EV-1 electric car (made famous by the film Who Killed the Electric Car?), as well as the former head of GM’s Corvette division — and set out to build an affordable, best-in-class electric car.

To raise money, he turned to his former Goldman Sachs colleague Steven “Mac” Heller, who is now chairman of Coda and before his retirement in 2002 was the worldwide co-head of Goldman’s investment-banking division. A group of prominent investors soon followed. Former Goldman CEO and ex-Treasury Secretary Hank Paulson is an investor, along with Tom Steyer of Farallon Capital; Mack McLarty, Clinton’s White House chief of staff; John Bryson, a former U.S. Secretary of Commerce and now an adviser at KKR; and Klaus Tschira, founder of German software giant SAP. Board members include former BP CEO Lord John Browne, now a managing director at the New York City private equity firm Riverstone Holdings, and Daniel Weiss, the founder of the Los Angeles private equity firm the Angeleno Group.

Though Heller’s background was Wall Street, he wasn’t worried about the complex challenges of starting a car company. “I grew up in Dayton, Ohio, three or four miles away from a GM (GM) plant. I was not confused about the complexity of the auto business. We thought the big automakers might be late getting into the EV business and saw an opportunity.”

Heller was intrigued because he saw Coda as a way to help tackle climate change, not to mention America’s dependence on foreign oil. He soon warmed to Czinger’s business plan. The idea was to create a virtual car company that excelled in engineering and design — and outsource most of the manufacturing to China. With the $125 million the company raised in early rounds (to date: more than $320 million), Czinger set up an engineering studio in Santa Monica, partnered with China’s Lishen, now the third-largest battery maker in the world, and formed a partnership with Harbin-based car maker Hafei. Czinger was betting he could keep costs low by having Hafei build the car’s body and chassis, and Lishen the battery cells. Final assembly would be in California. Coda’s competitive advantage would be its engineering, the ability to design the electronic controls and battery components that would make the electric vehicle safe and reliable. At the time, Czinger said that his virtual company could break even selling only 800 cars a month.

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If anyone seemed up to the job of making such a risky endeavor work, it was Czinger. Described by some as a force of nature, he holds degrees from Yale (where he starred on the football team) and Yale Law. Besides his time at Goldman Sachs, he worked at Bertelsmann and Webvan. Carmen Cozza, the legendary Yale football coach, described Czinger in his memoir, True Blue: “Kevin Czinger was the toughest kid to play football at Yale in my thirty-two years as head coach … maybe the brightest student and definitely the scariest individual.”

The irrepressible Czinger announced that Coda would be selling 14,000 cars a year by 2011. He also had a backup strategy: to license his state-of-the-art battery-control system to big car makers, including the Chinese. Reality soon set in. Automakers must set up elaborate supply chains, test for safety and durability, create dealer networks, and manage spare-parts distribution. That job would seem doubly hard for someone like Czinger, with no prior auto experience. In the fall of 2010, Coda had not hit its production target. More troubling, it had no product at all. At that point, Czinger stepped down, and Heller temporarily took over as CEO. “Kevin did a fabulous job leading us through the R&D stage,” explains Heller. “It’s not unusual to have a change of CEO between R&D and manufacturing.”

In January 2011, Coda said it was hiring Phil Murtaugh, a seasoned auto executive who had built GM’s China business into one of its most profitable divisions. Over a 10-year period Murtaugh grew revenue at GM China from $300 million to $7 billion. And Murtaugh knew supply chains — he now taps into hundreds of suppliers from more than 10 countries. This spring Coda rolled out its first cars, although the company — stung by its previously missed sales goals — will no longer talk publicly about targets.

Murtaugh has continued Czinger’s strategy of selling his battery technology to big car companies (he says he has letters of intent to supply batteries to a few major automaker but can’t yet reveal who they are). He has also signed an agreement with Beijing’s Great Wall Motors to develop a new electric car reported to be a compact crossover; it’s due to launch in 2014. Coda will provide the engineering for the electric powertrain system, and Lishen, its Chinese partner, will supply the batteries, while Great Wall will sell the all-electric under its brand in China. Coda will sell the U.S. version under its name.

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Coda, however, is facing some serious headwinds both here and in China. First, the Chinese car market in general is soft — with excess inventory piling up on lots around the country. Selling an all-electric in a market where consumers tend to live in high-rises without any place to park or charge their electric cars will be a challenge. Also, at a time when China’s economy is slowing, Beijing’s initiative to install public charging stations — the government’s 12th five-year plan states the nation will have 500,000 electric vehicles on the road by mid-decade — hasn’t rolled out as quickly as many had expected.

Another big challenge: a glut of lithium-ion-battery capacity. When electric-car euphoria was rampant a few years ago, LG, Johnson Controls (JCI), and other big battery makers began to build factories in anticipation of a boom that never materialized. Now some manufacturers are selling their batteries at a loss. That’s good news for electric-car makers, like Toyota (TM) and Ford (F), who buy their batteries for their electrics. Some battery makers have been selling them for as little as $350 a kilowatt-hour, although the cost of making them is around $500 to $700 a kilowatt-hour. That means Coda, which develops its batteries in its joint venture with Lishen, has an apparent cost disadvantage.

In the meantime, Coda keeps pushing ahead against fierce competition. Ford, Nissan, Mitsubishi, Toyota, and BMW have electrics. Nissan is the market leader with its Leaf. Pike Research estimates that it will sell 8,000 units in the U.S. this year. Also, plug-in hybrids — which don’t induce range anxiety — are gaining in popularity. Says Pike’s John Gartner: “Because of American driving habits, plug-in hybrids like the Prius and Volt should outsell all-electrics for the foreseeable future.”

How does the Coda stack up? Early reviews are positive, but Coda will have to prove that it can compete at scale with the global giants. Even Murtaugh must be nervous. Soon after becoming CEO, he hedged his bets by launching Coda Energy, a division that designs lithium-ion batteries for electric-grid storage. Example: The wind blows more at night. Utilities could store the power generated by wind turbines in batteries and use it during the day, when demand is higher. This is a potentially huge market. “Short term, we’ll be predominantly an EV business,” Murtaugh says. “In 10 years battery storage will dominate. So we’re really more of a clean-energy-technology company.”

Murtaugh must meanwhile figure out one of the most pressing problems about electric cars. They are still expensive — even after subsidies. A Republican victory in the fall could mean the end to a $7,500 federal tax credit and federal R&D battery programs. Murtaugh argues that even if that happens, California and 10 other states now have laws mandating that a small percentage of vehicles be zero emission. He’s also counting on the notion that new Presidents don’t always do what they say they will. “There’s a lot of broad support for electric vehicles from both Republicans and Democrats,” he says, “and I believe a change of administration wouldn’t make a difference.”

Coda’s high-rolling investors are hoping he’s right.

This story is from the September 24, 2012 issue of Fortune.