The Obama campaign said later in the afternoon they had no plans to apologize, and defended the criticism of Romney's campaign.

Obama's team has been pressuring Romney over a report Thursday in the Boston Globe that questioned when Romney severed ties with Bain Capital. Although both Romney and Bain have said that he left in 1999 to head the Salt Lake City Olympics, and no evidence has yet emerged to show that the Republican hopeful was involved in the day-to-day management of the firm, filings with the SEC show that Romney maintained the title of president and CEO.

Cutter said Thursday that this revelation meant that Romney was lying either in public statements or to federal regulators.

“Either Mitt Romney, through his own words and his own signature, was misrepresenting his position at Bain to the SEC, which is a felony, or he was misrepresenting his position at Bain to the American people to avoid responsibility for some of the consequences of his investments,” said Cutter. “And if that's the case, if he was lying to the American people, that's a real character and trust issue that the American people need to take seriously."

Campaign press secretary Ben LaBolt defended that comment in a statement Thursday, and said the president had no plans to apologize.

"Romney has said he had no authority or responsibility for managing Bain since February 1999, but that has been proven false.  He remained CEO, President, Chairman, sole owner and sole shareholder through 2001. Governor Romney either misled the American people about when he left Bain or misled the SEC," LaBolt said. "Which one is it?  The Romney campaign still won’t say.”

Bob Bauer, the Obama campaign's top lawyer, added that "under normal circumstances" federal regulators would consider opening an investigation into Bain's filings.

"Romney and Bain claim that he was not involved with Bain, but Bain and its portfolio companies in their required filings under the Securities Exchange Act continuously certified to the Securities and Exchange Commission precisely the opposite--asserting without qualification that he was a controlling person, fully in charge of Bain, under the Federal securities law," said Bauer in a statement. "Under normal circumstances, the question of the truth of this representation would result in an investigation by the SEC into possible criminal, as well as civil, violations of the law."

The Romney campaign has called the Globe report "untrue," and Bain Capital said in a statement Thursday that Romney was never involved in any of the company's work after he left to run the Olympic Games.

"Due to the sudden nature of Mr. Romney's departure, he remained the sole stockholder for a time while formal ownership was being documented and transferred to the group of partners who took over management of the firm in 1999," said Bain spokeswoman Charlyn Lusk in a statement. "Accordingly, Mr. Romney was reported in various capacities on SEC filings during this period."

The Romney campaign also issued a television commercial set to air in pivotal swing states Thursday that called Obama's repeated attacks on Romney's tenure at Bain "unfair and untrue."

— This post was updated at 5:05 p.m.