"A campaign based on falsehood and dishonesty does not have long legs," Romney said on Fox News.
"The president only has one thing going, and that is constant attacks on me. They're dishonest. They're misdirected. And I think the American people recognize that kind of politics as something of the past. It may work in Chicago, but it's not going to work across America."
Nonetheless the presumptive Republican nominee is still facing a barrage of questions, not just from Obama but from fellow conservatives, on two fronts: the true length of his tenure at investment firm Bain Capital, and his refusal to release more than two years of income tax returns.
Romney had a curious defence Monday on the tax return question, saying that releasing a multitude of past returns — something some Republicans are urging him to do — would simply serve to provide Obama with more ammunition.
The Obama campaign would be given "more things to pick through, more things for their opposition research to make a mountain out of, and to distort and to be dishonest about."
Amid a neck-and-neck race against Obama, Romney's also on the hot seat for a second week over his years at Bain Capital, the Boston-based venture capital firm he founded and helmed.
He has previously said he left the company in 1999 to run the Salt Lake City Olympics, but the Boston Globe unearthed documents last week that show Romney headed Bain until at least 2001.
Romney has vehemently denied having any active role in Bain following 1999. The date of his departure is significant since Romney has insisted he wasn't on board when Bain was outsourcing jobs and running companies that fell into bankruptcy from '99 to 2001.
One Romney aide said over the weekend that Romney had "retired retroactively," a line of defence met with almost instant ridicule by political pundits on both the left and right.
"He ended up not going back to the firm after his time in Salt Lake City. So he was actually retired from Bain," Ed Gillespie told CNN.
Kevin Madden, another adviser, said Romney's name had to remain on Security and Exchange Commission documents while he attempted to transfer the company's leadership to his partners.
"During that transition from 1999 to 2002 ... there was a duty to sign those documents," Madden said.
Obama, who campaigned in Ohio on Monday, defended his campaign's negative ads about Romney, one of which includes a clip of the former Massachusetts governor's cringe-worthy rendition of "America The Beautiful."
"The more detailed we get into what he's saying and what I'm saying — I think that serves the democratic process well," the president said in an interview broadcast Monday on "CBS This Morning."
Obama added his campaign has run a "whole slew of positive ads" about his administration's record and his objectives for a second term but the media doesn't give those spots as much attention.
The Obama campaign argues that Romney was in charge at Bain Capital when American jobs were outsourced to China. In a country where millions remain unemployed following a devastating economic meltdown, such allegations could prove toxic to Romney's campaign.
The Republican presidential hopeful has insisted the Obama campaign apologize for the line of attack.
Obama said Monday there would be no apology, and has said if Romney insists on heralding his business experience as preparing him for the White House, he should be prepared to answer tough questions about his Bain years.
Amid the Bain brouhaha late last week, Romney's campaign launched what also appeared to be an attempt at deflection: it suggested the candidate planned to pick a running mate earlier than usual, possibly weeks before the Republican convention in Tampa late next month.
The announcement lead to intense media buzz about which Republican has the inside track for the job, with the New York Times even reporting that Romney may unveil his pick as early as this week.
The Romney campaign denied the report on Monday, saying no decision has been made.
David Axelrod, Obama's chief campaign strategist, mused on Twitter about the vetting process for Romney's pick.
"Wonder how many years of back income tax returns Team Romney is asking from their VP candidates? Will their veep release more than Mitt?" he wrote.
Romney appeared to be attempting again on Monday to shift attention away from his Bain woes, accusing the Obama administration of rewarding donors with business opportunities.
"When millions upon millions of dollars are given by the Obama administration to the businesses of campaign contributors, that's a real problem, particularly at time when the middle class is really suffering in this country," he said on Fox.
"This is a tough time in America. But if you're a contributor to Barack Obama, your business may stand to get billions or hundreds of millions of dollars in cash from the government. I think it's wrong. I think it stinks to high heaven."
A conservative columnist urged Romney to continue to hit back instead of demanding apologies from Obama, mocking the candidate's comment last week that the president "sure as heck ought to say he's sorry."
"Ward Cleaver, call your office," Marc Thiessen wrote in the Washington Post.
"Obama is playing by the brass-knuckle rules of Chicago politics. Rather than calling for apologies, Romney needs to grab a bottle, break it on the bar and start fighting back."