President Obama’s campaign has spent many months trying to portray Mitt Romney as an unprincipled flip-flopper, a panderer to right-wing extremists and a greedy business executive. Then this week the ante was upped when one Obama aide suggested that Romney may be something worse: a potential felon.

The latest charge, made by deputy campaign manager Stephanie Cutter in a conference call with reporters, provoked immediate outrage from the Romney campaign, which, in the course of demanding an apology, called the president of the United States a habitual liar.

“The facts are clear: President Obama has a pattern of running dishonest campaigns, and the American people deserve better,” Amanda Henneberg, Romney’s deputy press secretary, said in an e-mail Friday.

The intensified hostility and persistent name-calling dominated the campaign news Friday and signaled that the presidential contest was entering a new phase, moving from relentlessly negative to downright nasty. And in a sign that the tactics were taking a toll on both sides, each candidate felt compelled to conduct a series of television interviews to respond to the criticisms from the other camp.

On Thursday, Cutter, citing media reports, questioned whether it was a potential felony for Bain Capital, the private equity firm Romney founded and led, to continue listing him as chief executive in filings to the Securities and Exchange Commission three years after he said he left, in 1999.

“Either Mitt Romney, through his own words and his own signature, was misrepresenting his position at Bain to the SEC, which is a felony,” Cutter said, “Or he was misrepresenting his position at Bain to the American people to avoid responsibility for some of the consequences of his investments.”

In an interview with the Washington ABC affiliate WJLA, Obama defended his campaign’s tactics: “Ultimately Mr. Romney, I think, is going to have to answer those questions,” Obama said, “because if he aspires to being president one of the things you learn is, you are ultimately responsible for the conduct of your operations. . . . That’s probably a question that he’s going to have to answer and I think that’s a legitimate part of the campaign.”

Romney’s campaign called the new attacks “reckless” and said they were evidence that the Obama side was “unraveling.”

But opinion polls suggest that Romney has been hurt by the Obama Bain attacks in key swing states and some Republican strategists have fretted openly that Romney has not responded forcefully enough.

On Friday, in a surprising move for a candidate who prefers tightly choreographed events, Romney sat down with five television networks to respond to the Obama attacks. Romney explained that he gave up managing Bain in 1999 and relinquished all control of the firm despite maintaining an “ownership stake.”

“This kind of statement from the Obama team is really shocking,” Romney told CBS News, referring to the felony charge. “It’s ridiculous, and it’s beneath the dignity of the presidency.” On ABC News, Romney said Obama “ought to say that he’s sorry for the kinds of attacks that are coming from his team.”

The racheting up of the rhetoric is perhaps a predictable consequence of millions of dollars in attack ads over the past several months. Elizabeth Wilner, a vice president of Kantar Media, which tracks political advertising, said nearly every advertisement run by the two campaigns across the country on Thursday was “negative” in tone and message.

And the sheer volume of those ads has, in some cases, doubled since four years ago. For example, the campaigns, along with the independent super PACs aligned with them, had run 1,640 television ads in Columbus, Ohio, a key battleground, in the first 12 days of July. That compares with 845 ads in 2008 and 462 in 2004, Wilner said.

“There is a reason why people use negative ads — they work,” Wilner said. “People say they can’t stand them and it turns them off. But while [the ads] may make people feel cynical about the process and sour them on politics, they eventually create an impression.”

On Friday, it was more of the same. Obama’s campaign released a Web video titled “Mitt Romney’s Bain Secret Exposed,” again questioning whether Romney relinquished control of the firm in 1999. And Romney’s campaign countered with “What Happened?” using video clips of Obama denouncing personal attacks in 2008 to charge that he had strayed from his pledge to remain above the fray.

In addition to the advertisements, the two sides have engaged in a constant cycle of taunting in which almost nothing is too petty for the campaign playground. On Friday, the Romney campaign bus circled a high school in Virginia Beach just before Obama arrived to give a speech. (At one Obama event in Cleveland last month, the Romney bus even honked its horn.)

For its part, the Obama campaign has repeatedly ridiculed Romney for refusing to release 12 years of his tax returns.

“Mitt Romney wants you to show your papers, but he won’t show us his,” Vice President Biden told Latino activists at the National Council of La Raza conference on Tuesday, simultaneously chiding the GOP challenger on his position on immigration and IRS disclosures.

By no means has the 2012 campaign devolved into the nastiest on record. In fact, there is a long history of brutal presidential contests, said Gil Troy, a presidential historian from McGill University in Montreal who has written extensively on the subject. He cited Andrew Jackson being accused of murder and adultery in 1828 as but one example.

More recently, a political action committee supporting George H.W. Bush in 1988 produced the infamous “Willie Horton ad” that accused Democrat Michael Dukakis of being lenient on violent crime. And in 2004, an outside group called Swiftboat Veterans for Truth, aligned with George W. Bush, used an ad called “Sellout” to question challenger John F. Kerry’s patriotism after the Vietnam War.

“The holy grail for American politics is the search for the substantive campaign,” Troy said.

Troy said the Obama tactic reflected the “joy people take in not just pummeling political opponents but criminalizing them” in the post-Watergate, post-Iran-contra era.

But he warned that there are downsides to the strategy: “If I were advising the Obama campaign, I’d tell them to be careful about going legal because it can backfire on you. Romney can then get on his high horse and say this should be a campaign of ideas instead of false accusations of legality.”

Obama, too, has jumped at the chance to play up the GOP attacks against him. In his stump speech, the president has bemoaned the “scary voices” in the Republican ads that blame the sluggish economy on him.

“Over the next four months, you will be bombarded with more negative ads,” Obama told supporters at an elementary school in Poland, Ohio, last week. “You’ve got these super PACs — millionaires, billionaires writing $10 million checks, just pouring — raining down on my head.”

“It’s all right!” someone shouted sympathetically.

“It is all right because I’m tough,” Obama concurred. “I’m skinny, but I’m tough.”