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A top White House official clammed up Sunday under questioning about the extent of President Obama's involvement in investigating his administration's security leaks -- even as officials warned the leaks are so severe as to potentially trigger a cyberattack by Iran.

Further, Sen. Joseph Lieberman, I-Conn., on "Fox News Sunday," put added pressure on the administration over the leaks by breaking with the president and calling for a special counsel to investigate.

The two U.S. attorneys chosen from the Justice Department to investigate, Lieberman said, are "not enough" to avoid "any appearance of conflict of interest."

The investigation -- along with bipartisan concerns about that investigation -- is getting underway going into the height of campaign season. To that backdrop, White House adviser David Plouffe claimed on "Fox News Sunday" that the back-and-forth amounts to a "game of distraction."

He urged lawmakers to let the current Justice Department investigation run its course.

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Yet Plouffe also declined to answer two keys questions about that investigation.

Asked if Obama would order any member of his administration who may have been involved in the leaks to come forward -- as former President George W. Bush did following the leak of CIA agent Valerie Plame's name -- Plouffe would not say.

"Everyone is obviously going to participate in the investigation," Plouffe said. Asked the same question again, he gave the same answer.

Plouffe was subsequently asked, twice, if Obama would sit down for a full interrogation by investigators in this case.

The second time, Plouffe put his hand up and curtly told host Chris Wallace: "I'm not going to answer his particular involvement right now, Chris."

Plouffe, though, did offer a denial after being asked several times whether Obama authorized any of the leaks in question.

"No, of course he didn't," Plouffe said.

He said Obama has "zero tolerance for this kind of national security leak."

Recent leaks on sensitive programs have contributed to two New York Times stories, one on the campaign of cyberwarfare against Iran and one on the president's involvement in approving the "kill list" of terror targets for U.S. drone strikes -- as well as the Associated Press newsbreak on a foiled bomb plot out of Al Qaeda in the Arabian Peninsula.

Fox News has confirmed that investigations are currently looking into the leaks on the anti-Iran campaign and the bomb plot -- it's unclear whether any probe will examine leaks on the drone program.

Lieberman stressed the severity of these leaks, calling them the "worst in a long time."

He and former CIA Director Gen. Michael Hayden said the leak about the cybercampaign against Iran could invite a counter-attack.

"I think there's a danger that it may legitimize an Iranian or a terrorist counter-cyberattack on us, because we did it," Lieberman said.

Hayden said he could just envision the head of intelligence in Iran making the case to Iran's leaders to open such an attack following the publication of the Times report.