But it's unclear if Romney's new strategy will be enough to change the subject, particularly as several prominent Republicans joined Democrats in pushing Romney for more transparency.
Late Tuesday, Texas Gov. Rick Perry — who challenged Romney for the Republican presidential nomination — became the latest in a series of high-profile conservatives to pressure Romney to open his finances. Perry, who has released his tax returns dating back to 1992, said anyone running for office should make public as much personal information as possible to help voters decide.
The conservative National Review urged Romney to release additional tax returns even though it agreed with him that the Obama campaign wanted the returns for a "fishing expedition."
"By drawing out the argument over the returns, Romney is playing into the president's hands," the magazine said in an online editorial. "He should release them, respond to any attacks they bring, and move on."
Romney spokesman Kevin Madden said Romney will not bow to the pressure.
"The governor has gone above and beyond what's required for disclosure," Madden said. "The situation remains the same."
Former Gov. Tim Pawlenty, whose name has appeared prominently in speculation about Romney's choice to run for vice president, vigorously defended Romney's limited tax release stance in a nationally broadcast interview Wednesday.
"There is no claim or no credible indication that he's done anything wrong," Pawlenty, who was a two-term governor of Minnesota, said on "CBS This Morning."
Pawlenty accused Obama's campaign of "hanging shiny objects before the public and the press and the press is taking the bait."
"I don't think there's any secret to the fact that Mitt Romney has been successful and he's achieved success and he's paid a lot of taxes," he said.
Meanwhile, Romney's campaign was forced to apologize for a supporter's statement that questioned Obama's patriotism, underscoring the political risks associated with the newfound aggression.
In a conference call arranged by the Romney campaign, former New Hampshire Gov. John H. Sununu told reporters he wished Obama "would learn how to be an American."
He later apologized for the remark.
"I made a mistake. I shouldn't have used those words. And I apologize for using those words," he told CNN. "But I don't apologize for the idea that this president has demonstrated that he does not understand how jobs are created in America."
The Romney campaign concedes that many voters may support the release of his tax returns, but it's unclear whether that's an important enough issue to change their votes.
At the rally Tuesday outside of Pittsburgh, Romney's supporters didn't seem to mind.
"I'm more concerned about what Obama does with my money," said Phil Kearney, a semi-retired 70-year-old Republican from Latrobe, Pa. "Romney's a rich guy. We all know it. God bless him."
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