Mitt Romney offered new details Sunday on how he might pay for the 20 percent income tax cut he's proposed for all Americans if he's elected president.

Speaking at a private fundraiser in Palm Beach, Fla., Romney told supporters he would eliminate tax deductions for wealthy people who own second homes. His comments were overheard and first reported by reporters from the Wall Street Journal and NBC News who were standing outside the fundraising event on the sidewalk.

"I'm going to probably eliminate for high-income people the second-home mortgage deduction," Romney said, adding that he would also likely eliminate deductions for state income and property taxes as well, according to NBC's Garrett Haake.

"By virtue of doing that, we'll get the same tax revenue, but we'll have lower rates," the candidate explained, according to NBC. He also added that the benefit of lower rates is that small businesses "get to keep a larger share of what they're earning and plow it back in to hire more people and expand their business."

Romney also told donors he might eliminate the Department of Housing and Urban Development, saying it "might not be around later." He also said he would downsize the Department of Education, suggesting he would "consolidate it with another agency or perhaps make it a heck of a lot smaller," though he insisted he wouldn't get rid of it entirely.

"I'm not going to actually go through these one by one," Romney said, according to NBC News. "What I can tell you is, we've got far too many bureaucrats. I will send a lot of what happens in Washington back to the states."

A Romney aide, who declined to be named discussing the former governor's comments, said the candidate was merely throwing out policy proposals. But Romney's comments are notable because the presumptive Republican nominee has been hesitant to go into specifics about how he would implement his tax and budget cuts as president.

President Barack Obama's re-election campaign quickly pounced on Romney's comments.

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"Apparently Gov. Romney believes only high dollar donors have a right to know what programs he would cut," Ben LaBolt, an Obama campaign spokesman, said in an email to reporters.

The Obama campaign also slammed Romney for not making copies of his past tax returns public. In January, the Romney campaign released a copy of the GOP candidate's 2010 tax return as well as his preliminary 2011 return but declined to make previous years public. Romney's father, George, disclosed 12 years of returns when he sought the presidency—a fact the Obama campaign and its supporters have seized upon as evidence that Romney isn't being "clear" with the public.

Romney has defended his decision not to reveal additional tax returns, telling reporters that he doesn't want to provide more fodder for his political opponents.

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