WASHINGTON — The Obama election campaign has a politically loaded question it wants voters to think about: What is Mitt Romney hiding?

Not a thing, Romney says. The Democrats are just trying to change the subject from the weak economy.

It’s a newly intense back-and-forth as President Barack Obama’s campaign team tries to cast his Republican opponent as a secretive rich guy who keeps his money in offshore accounts and refuses to release more of his tax returns.

The coordinated push, which includes stinging criticism from Obama and Vice President Joe Biden, web videos and television advertisements, comes as the Democrats grasp for ways to gain an advantage in a closely contested election and overcome a steady stream of lackluster economic news.

Getting personal, Biden declared Tuesday that Romney was “making a lie of the old adage, like father, like son” by not meeting the standards his father, George Romney, set when he released 12 years of tax returns during his 1968 presidential bid.  

In a speech to Hispanic leaders in Las Vegas, Biden said of Romney: “He wants you to show your papers, but he won’t show us his.” It was a criticism that hit both Romney’s financial reticence and his support for an Arizona immigration law that allows police to check the immigration status of people they stop.

The Obama campaign also posted a video on YouTube Tuesday that asked: “How long can Romney keep information on his investments in overseas tax havens secret? And why did he do it in the first place?”

Romney aides have called the barrage of attacks an “unfounded character assault” by a campaign desperate to distract attention from a sluggish economy that threatens the president’s re-election prospects. And Romney insists his private financial records contain nothing illegal.

“I have followed the law,” Romney said Tuesday on Sean Hannity’s radio show. “I have paid my taxes as due. I have also disclosed through all of the requirements of the government, every asset which I own, fairly and honestly, recognizing, of course, not to do so would be not only wrong but illegal and criminal.”

Still, Romney has released only a single year’s federal return — for 2010 — along with an estimate for 2011. Other returns could contain information about accounts he has held in Switzerland, the Cayman Islands and Bermuda, and that has created an opening for Democrats to accuse him of being secretive and taking advantage of tax loopholes that aren’t available to average Americans.

“I think what’s important if you’re running for president is that the American people know who you are, what you’ve done and that you’re an open book,” Obama said Monday in a television interview.

The Obama campaign says its focus on Romney’s private finances isn’t about his wealth but about whether he is gaming the system and, if so, what it says about what he would do as president to address tax loopholes.

With less than four months until Election Day, Obama aides say they may run new television ads targeting Romney’s close hold on his financial records. The campaign spent more than $2 million in May on an ad titled “Swiss Bank Account” that ran in politically important Iowa, Ohio and Virginia.

Democrats say the sustained criticism of Romney’s financial secrecy is solidifying for voters the notion that the Republican challenger is out of touch with middle class economics. A Washington Post-ABC News poll out Tuesday showed Obama with an 11 point advantage over Romney as the one who “better understands the economic problems people in this country are having.” Among registered voters, 51 percent said Obama better understands versus 40 percent who said Romney does.  

But longtime Republican operative Charlie Black said the Obama team’s focus on Romney’s personal finances was a Washington-driven issue that was unlikely to resonate with voters who would rather hear the candidates talk about their plans for job creation and economic growth.

“What people want to know is, did Romney file all of the legally required disclosures, which he did,” said Black, an informal adviser to Romney’s campaign. “They already know he’s a rich guy.”

While federal laws require Romney to release a broad portrait of his personal finances, candidates are not required to release their personal tax returns, despite the longstanding precedent for doing so, first set by Romney’s father.

Obama released seven years’ worth of returns during his 2008 campaign.

Romney, who could be worth up to $250 million, would be among the nation’s richest U.S. presidents if elected. He made his fortune at Bain Capital, a Boston-based private equity firm that has become a key part of the argument for his White House bid. He hasn’t drawn a regular paycheck in more than a decade, however, and has instead lived off a series of investments.

Romney faced pressure to release details of his finances during the GOP primary from Republican opponents who warned that the issue could follow him into the general election.  

“If there’s nothing in there, why not release them, and if there is something in them, better to know now,” former House Speaker Newt Gingrich said in January.  

Romney did relent under party pressure and release his 2010 returns. That forced him to amend the personal financial disclosures he had filed earlier in the year because those documents didn’t mention a Swiss bank account or a series of funds that were set up in foreign countries. Romney has yet to release his 2011 tax returns; he filed for a time extension. His advisers say he’ll release them before the Nov. 6 election.

Romney’s financial filings include at least six Cayman-based funds, worth between $7 million and $32 million, run by Bain. More than a dozen other funds based in the Caymans and Bermuda showed up on his 2010 federal tax returns. His campaign says he pays the same taxes he would if they were based in the United States.

Romney closed his UBS bank account in Switzerland in 2010 as he prepared to run for president.