WASHINGTON — President Barack Obama and his allies escalated their attacks on rival Mitt Romney for refusing to release more of his tax returns, suggesting Tuesday that secrets in those files cost him the vice presidency four years ago and could embarrass him today. “What is Mitt Romney hiding?” asked a new Obama ad.

Obama’s new 30-second ad questioned whether Romney paid his “fair share of taxes,” though it offered no proof for the assertion. Campaign officials Tuesday defended the ad, saying the full story behind Romney’s investments won’t be known until his tax records are released.

“The ad raises the question that we won’t know, and it’s not possible for anyone to know, until he releases further years of tax returns and everybody is able to examine what is included in them,” Obama campaign spokeswoman Jen Psaki told reporters aboard Air Force One.

The Democratic National Committee piled on with a web video, trying to link Romney’s tax returns to his being passed over as Republican presidential nominee John McCain’s running mate in 2008.

The video said that McCain had access to 23 years of Romney tax returns, but then named Alaska Gov. Sarah Palin as his running mate. "What does John McCain know that the American people don’t?" the ad asks.

McCain on Tuesday called the inference “outrageous.”

The new barrage from the Obama camp sought to leverage an ever-louder drumbeat from the president’s camp – and some Republicans – for Romney to disclose more of his tax returns. Under pressure from Republican primary rivals, Romney released his 2010 returns and estimates for 2011. He’s asked for an extension of time to file the 2011 return and said Tuesday he’ll release it when it’s ready.

He’s refused to go further.

“The opposition research of the Obama campaign is looking for anything they can use to distract from the failure of the president to reignite our economy,” Romney told the National Review on Tuesday. “And I’m simply not enthusiastic about giving them hundreds or thousands of more pages to pick through, distort and lie about.”

But every day he persists, his refusal to release returns adds another chapter in the Democrats’ storyline to paint Romney as out of touch. Polls show Obama far ahead when voters are asked who best connects with ordinary Americans.

The tax return furor could help fuel that narrative. “The specifics of these things are never the big deal for the public,” said Andrew Kohut, president of the Pew Research Center. “Things that relate to the definition of him as an elitist with advantages, compared to the average person—that’s where these arguments resonate.”

Romney is trying hard to change the subject. On Monday, his campaign launched an effort to paint Obama as lavishing lucrative favors on friends and donors. “The president doesn’t understand how America works. He doesn’t understand how business works,” former New Hampshire Gov. John Sununu told reporters on a conference call Tuesday.

He added, “I wish the president would learn how to be an American.”

Obama campaign spokeswoman Lis Smith quickly shot back.

“The Romney campaign has officially gone off the deep end. The question is what else they’ll pull to avoid answering serious questions about Romney’s tenure at Bain Capital and investments in foreign tax havens and offshore accounts,” she said.

Sununu apologized later Tuesday. “I made a mistake,” he said on CNN. “I shouldn't have used those words. And I apologize for using those words.”

The Romney campaign’s message is having trouble breaking through the clamor for the tax returns, as even some Republicans join the disclosure chorus. Texas Rep. Ron Paul, a 2012 Republican presidential rival, told Politico a release is “what the people want.” Former Republican party chairman Haley Barbour called the return flap “a distraction, and he needs to get back to what matters.”

Romney’s best hope to quiet it down, unless he releases the returns, is to change the subject soon. His best chance, said Kohut, probably comes at the August 27-30 Republican convention.

“He can present himself to the public and get a huge audience” and offer his own, unfiltered agenda, Kohut said. That forum was a huge boost to other challengers who endured tough summers, notably Bill Clinton in 1992 and George H. W. Bush in 1988.