After nearly two weeks of heated debate over whether President Obama should attack Republican Mitt Romney’s tenure at a private-equity firm, Democratic leaders across the country say they are largely united behind the strategy, even as some concede an uncertain outcome and new polls show Obama has lost ground nationally.

The Democratic leaders, in numerous interviews over the last week, said they are hearing little or no resistance among the party faithful in their states to a strategy that Republicans have characterized as anti-capitalist. And Obama has no plans to back off; his campaign will roll out more stories in the coming weeks that advisers said will again show Bain Capital as a corporate menace that protects profits at the expense of people and jobs.

“He wanted to have this conversation,” Jim Burn, chairman of the Pennsylvania Democratic Party, said of Romney, the likely GOP nominee. “We’re going to have it. There should be no hesi­ta­tion or equivocation.”

In Nevada, one Democrat said voters direct most of the blame for the state’s persistently high unemployment and foreclosure rates at Wall Street, describing it as the “bogeyman” of the election. In Ohio, party leaders said a large blue-collar population is receptive to evidence that Romney focused more on profits than people. Even in New Hampshire, where unemployment, at 5 percent, is far lower than in the hardest-hit states, Raymond Buckley, the state Democratic chairman, said voters blame the “reckless behavior” of investors such as Romney for the declining fortunes of their friends and family elsewhere.

“Look at Nevada,” said Roberta Lange, the Democratic Party chairwoman there. “Obama is speaking to the things that are important to us. The foreclosure market. Jobs. Romney has been absent from Nevada.”

But in other battleground states — including Virginia and Colorado — officials in both parties said there may be a risk of alienating business-minded independents, even if to many Democrats the risks are worth it. Republicans in particular welcomed the debate over Bain. Virginia Gov. Robert F. McDonnell (R) said Obama may intend for the Bain argument to “galvanize his base.”

“But I think overall those policies aren’t resonating particularly well with independents,” McDonnell said.

Some Democrats in Virginia expressed concern that voters in the business-oriented suburbs around Washington would not coalesce around attacks on Bain. Sen. Mark R. Warner, a former cellphone entrepreneur, said in an interview that Bain is “a valid issue and debate” but also a company that “did a good job for their investors.” One prominent Virginia Democrat who requested anonymity to speak candidly said the Bain strategy is “risky” because it feeds an existing narrative among business leaders that the Obama administration is not friendly to their interests.

Such divergent observations suggest a geographic and economic divide over how Bain might play with voters.

Colorado Gov. John Hickenlooper, a Democrat and a successful restaurateur, said he made a point of telling Obama stories during his recent visit about the local entrepreneurial spirit. Hickenlooper said he was pleased that Obama also wove some of those entrepreneurial stories into his public remarks that day. He is among those who support the president’s message about Bain but concede that they do not know whether it will work.

“Does it really outsource a lot of jobs?” Hickenlooper said. “Does it downsize companies? That’s a message that, if it takes hold, is something that voters are going to respond to.”

But, Hickenlooper added, “it’s too early to tell which arguments are persuading people.”

Several new national polls show the Obama-Romney race tightening, despite several weeks of aggressive efforts by Obama to frame the election around his foreign policy accomplishments, his economic policies and Romney’s record at Bain.

Democrats said they always expected Romney to enjoy a small lift in the polls after his emergence from a bruising primary battle. They also pointed to polls in crucial battlegrounds, including Virginia and Ohio, where Obama’s fortunes have improved. Still, the tightening is a reminder, they said, that this race is going to be won and lost on how Americans feel about the economy. That makes the Bain argument essential even if it carries certain risks, they said.

Obama launched his Bain push two weeks ago, when his reelection campaign began an effort to portray in a negative light the private-equity company that Romney co-founded. The purpose, one Democratic strategist said, was to “kick the legs out of” Romney’s image as an “economic wizard.”

A two-minute ad that aired last week focused on a shuttered steel mill in Kansas City, Mo., and the workers who lost their jobs after it went bankrupt under the supervision of Bain. One former worker in the ad called Bain a “vampire” that “came in and sucked the life out of us.”

Like those in Virginia, Republicans in New Hampshire and Colorado said they believed the Bain attacks would not work among independent voters. In Colorado, where biotechnology and energy investments have driven economic growth for the past few decades, voters may see Obama’s message as an attack against the investments that have helped start-up ventures get off the ground.

Rep. Cory Gardner (R-Colo.) said he attended a roundtable session last week with about 30 bioscience companies, some with 10 employees and others with thousands, and said many there told him they viewed the Obama campaign’s attacks as a “shame campaign” against the private-equity and venture capital sectors.

“I think people in Colorado understand that this is attacking a very positive opportunity for Colorado, which is trying to find investment opportunities to help their small businesses,” said Gardner, who was elected in a swing district in 2010. “This is a very entrepreneurial state. The president’s campaign is at odds with the entrepreneurial spirit of Colorado.”

Sen. Kelly Ayotte (R-N.H.), also elected in 2010, said she hears the same thing from voters in her state.

“It’s punishing success, which to me doesn’t really resonate with people in New Hampshire,” she said. “Basically what you’re doing is trying to demagogue a whole industry that tries to rescue failed companies. For many of those failed companies it’s the last resort of ability to get financing and keep the company afloat before they try to declare bankruptcy.”

Ayotte said the Bain issue may be moot in her state because voters there are already familiar with Romney and his background, considering he served four years as governor of neighboring Massachusetts and spent considerable time campaigning in New Hampshire during the primary season.

“We have a very strong sense of him,” Ayotte said. “I think that that’s not going to resonate here. I don’t hear a lot about that when I’m out doing my town hall meetings as a primary issue in the election. I think it’s going to be a real question of looking at the president’s record and who’s going to perform better on the economy and the debt.”

But Lange, the Democratic party chairwoman in Nevada, said the local experience makes the Bain argument extremely powerful thanks to a single, familiar company that Bain invested in — the Stage department store chain, which filed for bankruptcy in 2000 and experienced significant job losses. The Obama campaign has made an issue of Stage, although it entered bankruptcy after Bain sold it and later recovered from its earlier setbacks.

According to Lange, the department store illustrates an inherent advantage of the president’s Bain strategy, which can be offered in specific regions with examples likely to resonate with local voters. The Obama campaign has taken that approach in Nevada, Ohio and Iowa, all important swing states.

Romney and other Republicans have offered up alternative examples of companies that prospered under the Bain’s leadership and have denied that Romney was involved in some of the examples Obama has cited.

Republicans also jumped at the chance to portray Obama as someone who does not get business. They defended Romney’s Bain years, distributing examples of when the company helped turn around businesses or get them off the ground. And they sharply attacked the president, saying he lacks an understanding of how the economy works.

Senate Minority Leader Mitch McConnell (R-Ky.) said he did not know whether the Obama campaign’s attacks against Romney will work to vilify the Republican challenger.

“This is their effort to turn Romney into Gordon Gekko, and I think they feel that that’s their best shot at making him unelectable,” McConnell said.

That approach made a few Democrats uncomfortable, including Newark Mayor Cory Booker and former Pennsylvania governor Ed Rendell, who said in widely circulated interviews that they were displeased with the tone of the attacks.

Both men later said that they, too, think Bain is fair game this year. (Rendell said he got a “thank you” from Obama’s campaign in Chicago.) And based on more than a dozen interviews with Democrats in key battlegrounds, there is little evidence that their initial discomfort reflects a widespread view.

Meanwhile, Obama’s focus on Bain has not wavered, and it is not likely to, campaign advisers said.

“This is not a distraction,” the president told reporters last week, tamping down Booker’s remarks from an earlier TV interview. “This is what the campaign is going to be about.”

For many Democrats across the country, that was what they wanted to hear.

“This is the conversation we need to have,” said Burn, the Pennsylvania party chairman. “I would be more concerned if the campaign decided the tack needed to change.”