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“Do we want to keep giving those tax breaks to folks like me, who don’t need them, or to give them to Warren Buffet — he definitely doesn’t need them — or Bill Gates, he’s already said ‘I don’t need them,’ ” Mr. Obama asked. “Or do we want to keep investing in those things that keep our economy growing and keep us secure? That’s the choice.”

Mr. Obama also said families earning less than $250,000 per year should not see their taxes rise. Taxes for all wage earners will go up in January unless the president and Congress agree on an extension of tax cuts signed into law by President George W. Bush in 2001.

Although Mr. Obama argues that the wealthy should pay a higher tax rate than the middle class, the vast majority of wealthier Americans do pay more. The Tax Policy Center, a nonpartisan think tank in Washington, said only 4,000 households in the U.S. by 2015 will have income of more than $1 million and pay tax rates lower than 15 percent. The average tax rate for the middle 20 percent of U.S. families in 2015 will be 15.9 percent, the center said.

Opponents say the Buffett rule likely would result in wealthy taxpayers paying higher capital gains rates, which would in turn hurt economic growth. White House economist Alan Krueger said taxpayers who would feel the brunt of the legislation are those who structure their income “so that the vast majority of it comes in the form of capital gains or dividends.” Mr. Romney just happens to be in that category.

Democrats believe the Buffett rule has populist appeal. But a poll released Monday by the centrist Democratic group Third Way found that, among voters who don’t hold a strong opinion of either Mr. Obama or Mr. Romney, only 15 percent said they would choose a candidate who emphasized income inequality. About 80 percent said they would be more likely to support the candidate who focuses on growth and opportunity.

The White House has shifted its rationale for imposing the tax increase. When he raised the idea last September, Mr. Obama said such a measure would help with deficit reduction.

But Jason Furman, one of the president’s economic advisers, told reporters Monday that the administration is motivated by restoring fairness to the tax system, and that the Buffett rule “was never our plan to bring the deficit down and get the debt under control.”

White House press secretary Jay Carney said Tuesday the Buffett rule would help to pay for education, infrastructure and other programs which, “under the Republican budget, would be slashed dramatically in order to give more tax cuts for millionaires and billionaires.” It would raise about $47 billion over 10 years.

The Senate measure would require households with income of more than $2 million a year to pay a minimum tax rate of 30 percent. Households with incomes between $1 million and $2 million also would pay more.

In all, the Buffett rule would affect about 217,000 households. Mr. Obama visited two such households Tuesday in South Florida to hit up wealthy supporters for campaign contributions.

In a gated community called Frenchman’s Reserve in Palm Beach Gardens, Mr. Obama greeted guests who paid $15,000 per couple at the home of former Raytheon International president Hansel Tookes.

One supporter apparently asked Mr. Obama about the exclusive home in Hawaii where he spends Christmas vacation with his family.

“I just rent that house,” the president said. “I don’t actually own it.”

Mr. Obama was to hold a $15,000-per-head fundraiser later Tuesday at the residence of class-action attorney Jeremy Alters in Golden Beach. Mr. Alters, who won a $410 million case last year against Bank of America regarding its overdraft fees, is being sued by his former nanny, who alleges among other things that he still owes her $20,000 in wages. The litigator has called the nanny’s lawsuit “nonsense.”

The president also dropped by a lesbian, gay, bisexual and transgender fundraiser to pose for photographs with about 50 supporters but wasn’t scheduled to give formal remarks, therefore the White House didn’t include it on his official travel schedule. Tickets for that event started at $2,500 apiece.

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