Updated 1:03 p.m. ET

Mitt Romney is brushing off Rahm Emanuel's claim that he's "whining" about attacks made by President Obama.

"Well, I think when people accuse you of a crime you have a reason to go after them pretty hard, and I'm going to continue going after him," Romney said today on Fox News. "What does it say about a president whose record is so poor that all he can do in the campaign is attack me?"

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Romney charged Obama with running a campaign based on "falsehood and dishonesty."

Obama defended his campaign tactics in a CBS interview that aired today. "The more detailed we get into what he's saying and what I'm saying, I think that serves the democratic process well," Obama told CBS.

In his Fox News interview, Romney went on to say it "stinks to high heaven" that Obama's campaign donors have benefited from their ties to the president and White House. He is sounding a theme of political cronyism that his campaign intends to play up over and over this week.

Chicago Mayor Emanuel, a former Obama chief of staff, said Sunday that the presumptive GOP presidential nominee should "stop whining" about the Obama campaign's attacks on his record at Bain Capital.

Obama deputy campaign manager Stephanie Cutter had suggested Romney committed a felony for stating one thing on government documents but saying another about his tenure at the private equity firm.

Also on Fox, Romney deflected calls to release more than two years of tax filings and turned the question back to a criticism of Obama's campaign tactics. He said John McCain and John Kerry weren't called on in their respective presidential campaigns to release multiple years of tax returns.

"The Obama people keep on wanting more and more and more -- more things to pick through, more things for their opposition research to try to make a mountain out of and to distort and to be dishonest about," Romney said.