One afternoon earlier this year, Rex ­Tillerson, the chairman and CEO of Exxon Mobil Corp., and Barack Obama, then president-elect, laid out very different visions of America’s energy future. With the days counting down to his inauguration, Obama told a crowd at George Mason University of his plan to double U.S. production of renewable energy by 2012—“to finally spark the creation of a clean-energy economy,” he said, to screams from the students in the audience. That pledge was a small part of a broad alternative-energy push that has swept into the White House along with Obama.

Nearby, at the Woodrow Wilson International Center for Scholars, Tillerson, a lanky Texan with a thick drawl and slicked-back silver hair, celebrated the earth’s “continued abundance” of oil, noting that humans have consumed barely a third of the planet’s available petroleum reserves. Oil and natural gas, he said, in a story line that Exxon Mobil has perfected over decades, will continue to supply nearly 60 percent of the world’s energy needs for the next 20 years. “Let’s be realistic,” Tillerson scoffed, when asked about Obama’s green-energy visions. “Let’s don’t fool ourselves!”

For years, critics have skewered Exxon Mobil for funding skeptics of global warming, claiming that its corporate denial campaign has endangered the planet. The world’s largest private energy corporation now must confront a different sort of climate change—the one in Washington. The question: Can Exxon Mobil survive Barack Obama?

The new president decries not just America’s dependence on “foreign” oil—the battle cry of politicians everywhere—but America’s dependence on oil, period. And he believes Exxon Mobil in particular, and Big Oil in general, is a key part of the problem. “I want to be clear,” Obama said shortly after taking office. “We have made our choice: America will not be held hostage to dwindling resources, hostile regimes, and a warming planet. We will not be put off from action because action is hard. Now is the time to make the tough choices.”

Yet if the energy landscape is transforming before our eyes, you wouldn’t know it from looking at Exxon Mobil or listening to Rex Tillerson. As the rest of the world stampedes to alternative energy and a popular new president rallies for it, the largest investor-owned oil company—the one with the biggest profit in history last year and $31 billion of cash in the bank—is standing stubbornly still. In 2008, Exxon Mobil spent about $26 billion on oil and gas development, plus another $32 billion buying back its own stock; spending on renewable-energy research amounted to a measly $4 million.

It probably shouldn’t be a surprise that the company’s prospects for the next decade or two are starting to look shaky. Exxon Mobil’s output and conventional reserves are declining, along with its share price, which is down about 17 percent since the beginning of 2008. In Silicon Valley, where venture capitalists and entrepreneurs are pouring their hearts, their souls, and billions of dollars into solar, wind, and electric-car investments, some in the clean-tech crowd have dubbed Tillerson the T. rex of the hydrocarbon age.

The nickname is fitting. Critics see Exxon Mobil itself as a hulking dinosaur that mastered the earth in one era but appears increasingly maladapted in the current one. “They’re dinosaurs, absolutely,” said Fadel Gheit, an influential oil analyst for the investment firm Oppenheimer & Co., when we sat down in his Manhattan office last summer, as oil prices were soaring. “They epitomize peak-oil theory: They can’t grow production. They can’t grow [conventional] reserves. They need to ask themselves, Where will they be in 50 years? What will they do when oil is gone? They need to reinvent the company.” With oil prices down, Gheit is more sanguine but adds in an email: “A national energy strategy is a must and three decades overdue, and the environmental issue must be a part of it. Exxon and all other energy producers and consumers must recognize that and cooperate in fixing the problem before it gets a lot worse.” ( View an interactive feature comparing Exxon Mobil's stance on peak oil to other industry leaders.)

By refusing to seriously invest in a world beyond oil, Exxon Mobil marks itself not merely as politically incorrect but as a company that seems oddly indifferent to the business risks of its intransigence. It seems increasingly likely that Obama and Congress will slap a price on carbon in coming years that could put oil at a competitive disadvantage to such carbon-free energy sources as wind, solar, and biomass. That could reduce demand for crude, sharply cutting its price.

The Obama administration wants to create incentives to put a million plug-in hybrid cars on U.S. roads by 2015. IBM’s Institute for Business Value says that by 2020, the number of globally manufactured automobiles powered by gasoline alone will plunge to 65 percent of the total from 95 percent today. Right now, Exxon Mobil isn’t built to live in that kind of future.

Exxon Mobil pumps more oil and natural gas more profitably than any other company. In 2007, its profitability, or in companyspeak, return on capital employed, exceeded that of Chevron, its closest rival, by almost 40 percent. One reason for this is its laserlike focus on oil—and a deep organizational aversion to anything that threatens the bottom line. Climate change? Overblown, Exxon Mobil has long claimed, bolstering its skepticism with a well-funded public-relations campaign to cast doubt on the causes and consequences of global warming. Peak oil? No way are we running out, assures Tillerson, who insists that the earth has plenty of hydrocarbons left to burn. Renewable energy? Pipe dream, the company asserts, not worthy of serious investment by an oil giant. “We’re not in that business,” Tillerson said flatly at the company’s annual meeting in 2007. “We’re in the business of oil and gas.”