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“He hasn’t paid a penny less in taxes of where these funds are domiciled,” he said recently. “His liability is exactly the same as if he held the fund investments directly in the U.S. As a U.S. citizen, he is accountable for U.S. taxes. Some investments in some foreign countries can be tax havens. But Mitt Romney does not hold any such investments.”

Mr. Madden’s explanation wasn’t enough for Democrats such as Sen. Richard J. Durbin, Illinois Democrat. Appearing on CBS’ “Face the Nation,” he said offshore accounts prove Mr. Romney is either a tax dodger or that he doubts the economic strength of the U.S.

“There is just no way to explain it. You either get a Swiss bank account to conceal what you’re doing or you believe the Swiss franc is stronger than the American dollar,” he said.

Mr. Romney’s surrogates quickly came to his defense on Sunday, putting the spotlight back on Mr. Obama and his lack of private-sector experience and failed promises to keep the nation’s jobless rate below 8 percent.

“We’ve got a president today who’s never run a business, never run anything including a lemonade stand before he was president of the United States,” Louisiana Gov. Bobby Jindal said on CBS.

He added that when voters head to the polls in November, they’ll remember the Obama campaign’s desperate attempts to divert attention from the economy.

“I think voters will consider all of the distractions thrown out by the Obama campaign,” Mr. Jindal said.

Another Romney backer, former Mississippi Gov. Haley Barbour, said that Sunday’s round of charges — along with previous attacks on Mr. Romney’s tenure as the head of private-equity firm Bain Capital — aren’t just meant to distract, but also meant to persuade the American people that he can’t be trusted.

“What’s wrong with Mitt Romney, from the left, is that he’s a bad person. Senator Durbin makes him sound like he’s dishonest,” Mr. Barbour said on “Face the Nation.”

The former Massachusetts governor “is a guy who has a spectacular career and record,” Mr. Barbour said.