Six months after Mitt Romney’s reluctance to release his tax returns tripped him up in the South Carolina Republican presidential primary, the now-presumptive nominee is once again grappling with whether to disclose more information about his personal finances amid mounting pressure from his opponents.

For days, Democrats have been demanding that Romney make public additional tax returns that could shed light on his fortune, which is estimated at $190 million to $250 million. President Obama’s reelection campaign and its allies are hinting at nefarious activity, suggesting that Romney has been hiding information pertaining to his Swiss bank account and investments in the Cayman Islands. A scathing editorial in the New York Times this week pressed a similar case.

The Democratic attacks are part of a broader effort to portray Romney as excessively secretive, an argument that escalated Thursday with fresh accusations that he did not leave Bain Capital, an investment company he co-founded, in 1999 as he has said.

The candidate submitted to public pressure during the Republican primaries and released his 2010 tax returns, and he has said he will release his 2011 returns later this year once they are complete. Although Romney has followed the law, he has not adhered to historical precedent. His father, George, released 12 years’ worth of tax returns when he ran for president in 1968, and other top-tier candidates have traditionally taken a similar approach.

For the Romney campaign, the calculation is complex, as his advisers are weighing the benefits of transparency against the potential problems he could face should the documents reveal — or even appear to reveal — that he has gamed the tax code.

For now, Romney’s advisers said that the candidate has been sufficiently transparent and that he has no plans to disclose additional tax filings. But with four months left until Election Day — and the near-certainty that Romney will face questions about his finances in any interviews and in the fall debates — his advisers might be forced to reevaluate their strategy if the issue damages his standing in the polls.

Even some Republicans are describing the Romney position as problematic. Former Mississippi governor Haley Barbour, a onetime party chairman, said this week that he would provide more than two years’ worth of documents if he were in Romney’s shoes.

Strategist Mark McKinnon said the candidate's reluctance to release his taxes feeds into the Obama campaign’s argument that Romney is hiding something and taking advantage of the system to enrich himself.

“I think it’s pretty obvious there is something in the records that is problematic or the Romney campaign would have turned them over by now,” he said. “And they are gambling that the heat they’ll take for not disclosing is less than the fire they’ll take for the information that will become public if they do disclose.”

In 2008, when Sen. John McCain (Ariz.), the Republican nominee, was considering Romney for his running mate, Romney reportedly sent McCain’s vetting team tax returns dating to 1985. “I’m a bit of a pack rat, so I had them all,” the Arizona Republic quoted him as saying.

Obama campaign aides said additional returns could be an opposition researcher’s gold mine, providing new details about Romney’s Swiss bank account, his holding in a Bermuda corporation and the scope of his partnership profits from Bain Capital. They also said that more disclosures could show whether Romney has conflicts of interest with tax policies he is proposing.

Democrats are leveraging Romney’s unwillingness to release more filings to create doubt in voters’ minds about Romney’s character, trustworthiness and business ethics.

Obama strategist David Axelrod said last week that Romney is “the most secretive candidate that we’ve seen, frankly, since Richard Nixon.” And on Tuesday, Vice President Biden told an audience of Latino voters, “He wants you to show your papers, but he won’t show us his. It’s kind of fascinating. So many questions.”

On Thursday, Senate Majority Leader Harry M. Reid (D-Nev.) told reporters that Romney “not only couldn’t be confirmed as a Cabinet secretary, he couldn’t be confirmed as a dog catcher, because a dog catcher — you’re at least going to want to look at his income tax returns.”

Romney and his campaign have done little to respond to such comments. His advisers rejected any suggestion that the issue could damage the candidate’s standing with independent voters, saying it is background noise that voters will see as a minor tactic to distract them from a larger issue: the economy.

“At a time when the nation is suffering through unemployment above 8 percent for longer than since the Great Depression . . . this attempt on the White House to shift attention away from real issues in the campaign is getting to the point of being desperate,” said former senator James M. Talent, a Romney policy adviser.

Romney long has resisted disclosing personal financial information. During his 2002 governor’s race in Massachusetts, releasing his tax returns was “a non-starter,” according to a former aide, because Romney “didn’t want people poking around in his personal financial business.”

“He just said, ‘I’m not going to do it. It’s not going to happen,’ ” said the aide, who spoke on the condition of anonymity to share private discussions. “He didn’t think it would hurt him, and he was proven right. He won that race.”

Rosalind S. Helderman in Washington contributed to this report.