On a conference call with reporters Ms. Cutter said Mr. Romney "is the most secretive person to run for president since Richard Nixon."
But Matt Rhoades, Mr. Romney's campaign manager, said that charge was so over-the-top that Mr. Obama needs to apologize for his entire campaign operation.
"President Obama's campaign hit a new low today when one of its senior advisers made a reckless and unsubstantiated charge to reporters about Mitt Romney that was so over the top that it calls into question the integrity of their entire campaign," Mr. Rhoades said in a statement. "President Obama ought to apologize for the out-of-control behavior of his staff, which demeans the office he holds. Campaigns are supposed to be hard fought, but statements like those made by Stephanie Cutter belittle the process and the candidate on whose behalf she works."
Ms. Cutter is a long-time political operative who worked for Sen. Edward M. Kennedy, worked for Sen. John Kerry's campaign in 2004 and now works for Mr. Obama.