(Nicholas Kamm/AFP/Getty Images | Joe Burbank/Orlando Sentinel/MCT/Newscom)

MILWAUKEE - The Obama campaign is embracing debate over President Obama's comments this week about changing Washington from the outside , saying the strategy has been "a hallmark of the president's leadership style" while criticizing rival Mitt Romney for suggesting he could affect change on his own.

"This is a fundamental difference in how they would govern," Obama campaign spokeswoman Jen Psaki told reporters today aboard Air Force One. "Mitt Romney seems to believe he can wave a magic wand and tell people what to do within the walls of Washington, and that that's going to make change happen in this country."

During the Univision forum Thursday, Obama said the "most important" lesson he learned in his first term is that "you can't change Washington from the inside."

"You can only change it from the outside," he said. "That's how I got elected, and that's how the big accomplishments, like health care, got done, was because we mobilized the American people to speak out. That's how we were able to cut taxes for middle-class families."

Romney pounced on the remark, saying that Obama - now on the "inside" in Washington - had thrown in "the white flag of surrender" on his pledge to change politics in the nation's capital.

"I will change Washington. I will get the job done from the inside," Romney said, appealing to voters' bipartisan frustration with legislative gridlock.

Psaki today welcomed the spirited 48-hour back-and-forth with Romney as an "opportunity" for the president to highlight an argument he first began making four years ago.

"A hallmark of the president's leadership style has been mobilizing and channeling the opinions and views and sentiments of the American people to bring change to Washington, D.C.," said deputy White House press secretary Josh Earnest.

Earnest cited passage of Wall Street reform legislation as an example of change Obama has affected with help from the "outside."

"We're talking about the voices of the American people up against entrenched special interests in Washington, D.C., that were used to calling the shots," Earnest said. "We had a situation where we mobilized the voices of the American people to ensure, for example, that we had things like a Consumer Financial Protection Bureau that would be an advocate for the voices of middle-class families.

"Mitt Romney might suggest that outside pressure is lobbyists for Wall Street banks, lobbyists for oil companies looking to protect their subsidies," he said.

Romney campaign spokesman Ryan Williams shot back, saying Obama failed to affect "change" on the most important issue to Americans: the economy.

"Instead of going to Washington and fixing the problems facing our country, President Obama has given up trying to change Washington and become part of the problem," Williams said in a statement to ABC News.

"As a successful businessman, Mitt Romney has developed the skills and determination needed to fix our broken government, create economic opportunity for the middle class and get real results for every American," he said.