But the White House says the changes were requested by Republican governors — including Romney — who wanted more autonomy from the federal government in distributing welfare funds.

"Perhaps his argument is with his past self and I suppose that should not be a surprise," Carney said, adding that an ad released Tuesday by the Romney campaign on the same subject was an "utter misrepresentation" of the president's policies.

"Hypocrisy knows no bounds," Carney added.

Jonathan Burks, Romney's deputy policy director, on Tuesday defended a 2005 letter signed by Romney that requested increased wavier authority to help states increase flexibility in implementation. On a conference call with reporters, Burke said the flexibility Romney was seeking was not related to the Temporary Assistance for Needy Families program's work requirements.

"The governors were not requesting a waiver of the key work requirement," he said.

The Obama campaign also criticized Romney for his attack in a statement released Tuesday.

"The truth is that the President is giving states additional flexibility only if they move more people from welfare to work — not fewer," said Obama spokeswoman Lis Smith in an email. "By falsely attacking a policy that both he and his Republican allies have supported for years, Romney is once again flip flopping on a position he took in Massachusetts, and demonstrating that he lacks the core strength and principles the nation needs in a President."

But Republicans continued to hammer the president Tuesday afternoon, with a spokeswoman for the Romney campaign pointing to prior statements of Obama's critical of Clinton-era welfare reforms.

“When President Obama took unilateral action to begin dismantling welfare to work, it wasn’t an isolated incident," said Romney spokeswoman Amanda Henneberg in an email. "Throughout his career, President Obama has demonstrated hostility for the historic welfare reforms passed by President Clinton and Republicans in Congress. Unlike President Obama, Mitt Romney has always been a strong supporter of welfare reform and, as president, will immediately restore work requirements to welfare.”

—Mike Lillis contributed.