Three decades after private-equity firms transformed American business, American politics is finally catching up — breathless and bewildered.

For the past week, the spotlight of the presidential campaign has fallen on Mitt Romney’s 15 years as an executive at the private-equity firm Bain Capital. President Obama has at times portrayed Romney, his likely GOP challenger, as a kind of pinstriped vampire who sucked profits out of hapless companies while factories closed and workers suffered.

Romney has cast himself as an enabler of American dreams: His campaign says his work at Bain built businesses and created tens of thousands of jobs.

But both campaigns, as well as others in Washington, still seem to be struggling with how to talk about an industry that exaggerates both the good things and the bad things about capitalism.

On Tuesday alone, Democratic Sen. Mark R. Warner (Va.) said Romney’s firm “did what they were supposed to do.” But Rep. James E. Clyburn (S.C.) — the third-ranking Democrat in the House — likened Romney’s work at Bain to rape. “There’s something about raping companies and leaving them in debt. . . . I have a real serious problem with that,” he said on MSNBC.

The Obama campaign said it “strongly disagreed” with Clyburn’s characterization.

Rep. Cathy McMorris Rodgers (Wash.), vice chairman of the House Republican Conference and a Romney supporter, condemned Clyburn’s comments, saying in a statement that “using the word ‘rape’ to describe Gov. Romney’s record as a job creator is offensive, especially to women.”

In a speech later in the day, Vice President Biden argued that Romney’s work in private equity is irrelevant for the position he is now seeking.

“Your job as president is to promote the common good,” Biden said in Keene, N.H. “That doesn’t mean that private-equity guys are bad guys; they’re not. But that no more qualifies you to be president than being a plumber.”

Romney’s campaign said Tuesday that by attacking Romney’s tenure at Bain, Obama is guilty of an “assault on free enterprise” itself.

Romney’s time at Bain Capital is a keystone of his political persona: It defines a candidate who tries to avoid being defined by his wealth, his liberal home state of Massachusetts or his Mormon religion.

In 2008, Obama cast himself as someone who understood politics well enough to fix it. In 2012, Romney has used Bain to make the same argument about the economy.

“I know what it means to meet a payroll,” he wrote in the introduction to his economic plan. “I know why businesses hire people, and why they become forced to lay them off.”

But all this might be easier if Romney had dealt in pizzas and not pizza companies (Bain purchased Domino’s Pizza on Romney’s watch). The nature of private equity — its unsentimental focus on “creating wealth,” and the long distance between Bain executives and the workers they oversaw — has complicated the story Romney wants to tell.

In general, private-equity firms invest in other companies, and then use their own smarts and borrowed money to remake them, for sale at a profit. In some cases, that can mean hiring new management, or providing money for a new factory or marketing effort.

Private-equity companies have been a force in American business since the hostile-takeover spree of the 1980s. They boomed again in the late 1990s and early 2000s, as the lifeblood of their efforts — easy credit — became easier than ever.

Romney’s campaign has touted Steel Dynamics, an Indiana company that built its first plant after Bain’s investment. “Steel Dynamics started with an empty field and a big dream,” the campaign’s ad says. But, the ad says, the dream came true only after “Mitt Romney’s private-sector leadership team stepped in.”

But sometimes, a private-equity firm may shutter a factory or cut a workforce to reduce costs.

And even when the bet goes bad and the company closes, the private-equity firm can often walk away unencumbered. Sometimes, it even walks away with more money than it started with.

Under Romney’s leadership, Bain bought steelmaker GS Industries in 1993 and loaded it with debt while paying millions to Bain investors. It declined and in 2001, after Romney was no longer managing Bain, the company filed for bankruptcy, and more than 700 workers lost their jobs. Obama’s campaign has highlighted this company in an ad where one ex-worker says, “It was like a vampire came in and sucked the life out of us.”

Howard Anderson, a lecturer at the Massachusetts Institute of Technology’s Sloan School of Management, said that Romney’s allies often say he “created jobs” while at Bain. “No, you guys build wealth,” he said.

“Sometimes you build jobs. Sometimes you eliminate jobs,” Anderson said Tuesday. “What private equity is — and what Bain and the other guys do — it’s the best of capitalism, and it’s the worst of capitalism. . . . Capitalism doesn’t try and do the right thing. Capitalism can be very destructive.”

The two sides of the private-equity business — its booming successes and its deep, devastating failures — make it hard to caricature it as all good or all bad.

The industry has been worried about this moment for a long time. Anticipating Romney’s candidacy, an industry group began to prepare a stepped-up lobbying and public education campaign last summer. It titled the campaign “Private Equity at Work” and targeted political “opinion leaders,” including lawmakers.

“The industry is not widely understood by the general public and even by some on Capitol Hill,” said Steve Judge, president and chief executive of the Private Equity Growth Capital Council, which lobbies for leading private-equity firms.

For both parties, the struggle to frame a moral argument about private equity could affect the vote in November. In a new Washington Post-ABC News poll, 21 percent of voters said that Romney’s work with Bain was a reason to support him. The same share said it was a reason to oppose him.

And 54 percent — the targets of all this messaging — said it wasn’t a major factor.

This argument also could affect campaign fundraising: Although politicians often seem to have just discovered private equity, their campaign treasurers clearly found it long ago. In 2008, the industry supported Obama over Sen. John McCain (R-Ariz.) and gave more to Democrats overall than Republicans.

But this year, the private-equity industry has contributed $23 million — with more than 75 percent of that going to Republicans.