Obama weighed in Monday as the dust-up lit up social network sites, calling Booker an “outstanding mayor” but insisting he would continue to talk about Romney’s experience at Bain Capital.

“It’s important to recognize this issue is not a distraction,” the president said. “It’s part of the debate we are having in this election.”

The episode, which delighted Republicans while causing a headache for Obama, illustrated the difficulty a presidential candidate faces in controlling his or her message in the era of YouTube and Twitter. It also raised questions about how much campaigns should be held responsible for what their supporters — known as “surrogates” in political-speak — say or do.

“Maintaining message discipline with surrogates has always been a challenge of the modern campaign. In the era of social media it is an exercise in futility,” said Chris Lehane, a spokesman for Democrat Al Gore’s 2000 presidential bid. “Most surrogates are significant people in their own right with their own views, own constituencies and own press corps, and are used to speaking for themselves and not conditioned to the idea that whatever they say or do will become attached to a presidential candidate.”

That was the case for Booker, who has an active social media presence and is eyeing a run for statewide office in New Jersey, where many bankers and private equity investors live.

His effort to soften the blow of his comments Sunday on NBC’s “Meet the Press” didn’t seem to satisfy Obama’s team. Campaign strategist David Axelrod told MSNBC a day later that Booker was wrong and Romney’s experience at Bain “speaks to an economic theory that isn’t the right economic theory for the country.”

Meanwhile, a gleeful Republican National Committee bought ads on Twitter drawing attention to Booker’s comment, and launched an “I Stand with Cory” petition that links signers to a video him.

Almost everyone who speaks on behalf of a candidate is dubbed a surrogate, whether they are close advisers, television pundits or donors eager to make their opinions known. Some surrogates hew closely to the campaign’s talking points. Those who don’t quickly find themselves in the hot seat.

That’s what happened to Romney strategist Eric Fehrnstrom, who told CNN in March that the campaign would “hit a reset button” once Romney became the Republican nominee.

“It’s almost like an Etch A Sketch,” Fehrnstrom said, referring to the children’s toy. “You can kind of shake it up, and we start all over again.”

The remark, which immediately went viral on the Internet, seemed to reinforce a narrative that Romney has long battled — that the former Massachusetts governor is a shape-shifter who can’t be trusted as a true conservative. Campaign advisers insisted Fehrnstrom was talking about the logistics of running a general election campaign, not Romney’s core principles. But Democrats used the moment to assail Romney anyway.

Celebrities — often helpful in drawing attention and cash to a candidate — can also cause headaches for campaigns.

Talk-show host Bill Maher, who has contributed $1 million to a super political action committee supporting Obama, posted a message on Twitter on Monday that referred to Romney’s Mormon faith as a “cult.” Obama’s campaign has said Romney’s religion should not be part of the campaign.

Maher also stirred controversy last month when he used an expletive on his HBO program to argue that Romney’s wife, Ann, hasn’t worked outside the home. Republicans called on Obama to distance himself from Maher and said the super PAC, Priorities USA Action, should return the celebrity’s money.

That dust-up was similar to another from last month, when Obama supporter Hilary Rosen said Ann Romney “had never worked a day in her life.” Obama’s campaign swiftly repudiated the comment and sought to distance itself from it even though Rosen has no role in the campaign. Obama’s team feared the absence of a strong repudiation of Rosen’s remarks would both turn off women voters and signal that attacks on wives were acceptable.

Romney’s campaign had its own problems with a celebrity surrogate when Ted Nugent, a rock music star, made provocative comments about Obama.

Nugent met with Secret Service representatives after a speech to the National Rifle Association in which he referred to Obama’s “evil, America-hating administration” and urged voters to “chop their heads off in November.” Nugent added, “If Obama is elected, I will either be dead or in jail.”

Romney’s campaign, which sought and publicized Nugent’s endorsement, distanced itself from his comments. “Divisive language is offensive no matter what side of the political aisle it comes from,” Romney spokeswoman Andrea Saul said. “Mitt Romney believes everyone needs to be civil.”

That wasn’t enough for Democratic National Committee Chair Debbie Wasserman Schultz, who called on Romney to “condemn Nugent’s violent and hateful rhetoric immediately.”

Super PACs, which can raise and spend unlimited sums and are legally prohibited from coordinating with the candidates they support, have emerged as surrogates of a sort and have further complicated efforts by campaigns to stay on message.

Romney was forced to answer for — and repudiate — an ad campaign under consideration by a conservative-leaning super PAC showcasing Obama’s relationship with his controversial former pastor, the Rev. Jeremiah Wright. Joe Ricketts, the billionaire founder of TD Ameritrade Securites, had been weighing a $10 million contribution to the effort but said after it became public that he did not want to participate in such an effort.

Neither did Romney, who said: “It’s the wrong course for a PAC or a campaign.”

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“The idea that these groups are independent is a fiction in reality terms and, we believe, a fiction in legal terms,” said Fred Wertheimer of Democracy 21, a campaign finance reform advocacy group.

The back-to-back Obama spots, to run in four of the same five general election swing states, are a sign of the new world of campaign finance, where so-called super political action committees have wide leeway to spend as much as they want to help or hurt candidates. And the ads also cast new light on the cozy relationship between campaigns and these groups, raising questions about how independent they are from each other.

The coziness isn’t limited to Democrats. A Romney-aligned super PAC is keeping him competitive on TV as he regroups for the general election. And the relationship between that group — Restore Our Future — and the presumptive GOP nominee was on vivid display during the Republican primaries, when the group spent $36 million on ads assailing the former Massachusetts governor’s rivals.

Super PACs, born of a 2010 Supreme Court decision easing political spending rules, can raise and spend unlimited donations as long as they don’t coordinate directly with the campaigns they support. But the lines are often blurry: The pro-Obama super PAC Priorities USA Action is run by former Obama White House aides, while Restore Our Future is staffed by former Romney advisers.

Strategists for the super PACs insist they are operating independently and are not relying on signals from the presidential campaigns as to what advertising strategy to pursue. But campaign finance watchdogs are crying foul, arguing that super PACs have effectively become high-dollar shadow campaign operations for candidates otherwise constrained by much stricter federal campaign finance rules.

Said Wertheimer: “Candidate-specific super PACs are simply arms of the presidential campaigns and need to be treated as such and be subject to contribution limits.”

Republicans have generally welcomed the emergence of super PACs, and several GOP-leaning groups spent millions to take control of the House and pick up six Senate seats in 2010. Obama sharply criticized the emergence of super PACs that year but ultimately green-lighted contributions to Priorities USA Action after it became clear that his campaign and other Democrats would be vastly outgunned otherwise.

Tuesday’s new ad launched by Priorities USA Action highlights the failure of GST Steel, a Kansas City, Mo.-based company purchased by Bain Capital that went bankrupt and laid off 750 workers in 2001. A day earlier, the Obama campaign announced it was targeting Bain’s management of GST Steel in a two-minute ad.

Priorities USA Action is spending $4 million to air the new ad, while the Obama campaign committed just under $100,000 to run its commercial. But Bill Burton, a former Obama White House aide who now heads Priorities USA Action, said the timing of the two ads was a coincidence and his group had not waited for the Obama campaign go after Bain before making a similar attack.

“It wasn’t a matter of waiting for anything, this was our strategy,” Burton said, adding that the ad had been shot in February and the group has several more it plans to air related to Bain.

“There are four or five examples that are particularly telling of how Mitt Romney made decisions when he was in private business. We had planned on telling this story regardless,” Burton said.

Priorities USA Action’s might may be limited — the group has struggled to raise money, taking in about $10 million through its super PAC and affiliated nonprofit arm by the end of March. The group has spent $2.7 million on ads in May, compared to $28.6 million by the Obama campaign, according to data provided by ad buyers to The Associated Press.

Republican-leaning groups, by contrast, spent about $14 million on commercials in the same period. About $4.3 million was spent by Restore Our Future, which has raised at least $51 million since its inception to support Romney. The Romney campaign has spent no money on TV ads since Romney’s Republican opponents dropped out, clearing his path to the nomination.

Obama’s campaign opened the month of April with more than $100 million in the bank, a 10-to-1 fundraising advantage over Romney. But the president’s edge is minimized by the campaign cash raised by Restore Our Future and other Republican-leaning super PACs, which have pledged to spend hundreds of millions of dollars to help Romney.

Carl Forti, who heads Restore Our Future and served as political director for Romney’s 2008 presidential bid, said the group does not need to coordinate with the Romney campaign to know how to make the best use of resources.

“We’re politically experienced people, we know what Obama’s vulnerabilities are and what we need to do to help Mitt win,” Forti said. “Just because we can anticipate what they need and where they are going, it doesn’t mean it’s coordinated.”

Forti also serves as a strategist for American Crossroads, a super PAC with ties to Karl Rove, President George W. Bush’s longtime political director. Crossroads has announced plans to spend as much as $300 million to influence the presidential contest.

While the Republican groups may not coordinate directly with the Romney campaign, they do coordinate with each other. Leaders of some leading Republican super PACs attend a monthly meeting hosted by Crossroads to share information and devise strategy.

Paul Ryan of the Campaign Legal Center, an advocacy group, said super PACs are operating under a fig leaf of independence that does not hold up under scrutiny.

“Super PACs have little or no true independence, that’s why large contributions to super PACs pose just as great a threat of corruption as they would if given directly to the candidates,” Ryan said. “To put it bluntly, there’s no real need for them to coordinate as the law defines it in order to run an incredibly effective ad campaign using unlimited, potentially corrupting contributions.”

The new Priorities USA Action ad is running on TV in Colorado, Florida, Ohio, Pennsylvania and Virginia. The Super PAC also began a website with its version of Romney’s record as CEO of Bain Capital. The Obama campaigns ad is to air in Iowa instead of Florida.

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Thomas reported from Washington.

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