In a congressional hearing, Retired Brig. Gen. Robert Lovell, who was in the U.S. military's operation center during the attack, said the U.S. should have tried to do more to counter the attack that led to the deaths of four Americans.
"There are accounts of time, space and capability discussions of the question, could we have gotten there in time to make a difference," Lovell told the House Oversight and Government Reform Committee. "Well, the discussion is not in the 'could or could not' in relation to time, space and capability -- the point is we should have tried. As another saying goes, 'Always move to the sound of the guns.'"
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Lovell said there was "desperation" in the operations center "to gain situational awareness and to be able to do something to save people's lives."
Asked about Lovell's comments, White House press secretary Jay Carney cited an interview that former Chairman of the Joint Chiefs of Staff Mike Mullen had given to House Oversight Committee staff, in which he said that his review concluded the military had done everything possible.
"He made abundantly clear that in his view -- again, an admiral, a chairman of the Joint Chiefs of Staff appointed by President George W. Bush -- that the military did everything that it could and acted appropriately in every way in response to this attack," Carney said.
House Armed Services Committee Chairman Howard "Buck" McKeon, R-Calif., also pushed back against Lovell's testimony. In a statement, McKeon said he appreciated Lovell's service but noted that "Lovell did not serve in a capacity that gave him reliable insight into operational options available to commanders during the attack, nor did he offer specific courses of action not taken."
"The Armed Services Committee has interviewed more than a dozen witnesses in the operational chain of command that night, yielding thousands of pages of transcripts, e-mails, and other documents," McKeon said. "We have no evidence that Department of State officials delayed the decision to deploy what few resources DoD had available to respond."
Meanwhile, back in the Oversight Committee hearing, Rep. Jason Chaffetz, R-Utah, slammed the administration for failing to "run to the sound of guns" and instead "issuing press releases."
Chaffetz also criticized administration officials for suggesting that the attack was spurred on by an anti-Muslim video. "The military, the CIA, the CIA station chief, the State Department; all of them, the facts at the time, Mr. Chairman, the facts do not point to a video," he said. "That only comes from the White House."
His criticisms come one day after new emails were released, shedding more light on the way the White House attempted to frame the discussion about the attack and general Mideast turmoil.
Carney also pushed back against Republicans for continuing to politicize the attacks in Benghazi.
"What we have seen since hours after the attack, after the attack, beginning with a statement by the Republican nominee for president, is an attempt by Republicans to politicize a tragedy. And that continues today and yesterday," he said.
The focus should turn to assessing how to prevent a similar incident in the future, Carney said, although he maintained that the newly-released emails were not an indication the administration had tried to cover up their involvement in editing the talking points. He said it was not included in a previous request for emails related to the Benghazi aftermath because they were "explicitly about the broader areas, separate from the attack on Benghazi."
Still, Sen. John McCain, R-Ariz., on Thursday went so far on Fox News to suggest the emails show the administration was staging a "cover-up." The emails framed the attack "all in line with a reelection campaign rather than the facts surrounding the tragic deaths of four brave Americans," he said.
House Minority Leader Nancy Pelosi, D-Calif., told reporters Thursday that the emails were simply a distraction from real issues like immigration reform, renewing long-term unemployment insurance or raising the minimum wage.
"Diversion, subterfuge, Benghazi, Benghazi, Benghazi," she said. "Why aren't we talking about something else."
CBS News' Rebecca Kaplan contributed to this report.