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Capitol Hill lawmakers disagreed Sunday on the importance of U.S. Ambassador Susan Rice’s role in the aftermath of the fatal Libya attacks, with independent Sen. Joe Lieberman arguing Republicans are taking a short-sighted approach by focusing on her public explanation of events.

Rice said publicly five days after the Sept. 11 attacks on two U.S. outposts in Benghazi, Libya, that the strikes were “spontaneous” and sparked by outrage over an anti-Islamic film.

Evidence including Capitol Hill testimony last week by former CIA Director David Petraeus showed that U.S. officials knew almost immediately that terrorist-related groups were involved.

“Nobody could deny … it was a terrorist attack,” Lieberman said on "Fox News Sunday." "But I think we are focusing on questions that are ... not the most significant. Of course, there was a terrorist attack.”

Lieberman, I-Conn., said the more important questions are why amid intelligence showing Al Qaeda other militant or terror-related groups coming into eastern Libya did the United States leave State Department personnel there without security. And why didn’t the Defense Department have nearby resources to come to their defense.

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Republican lawmakers think the White House changed the unclassified CIA report that Rice used as talking points for her five TV interviews Sept. 16.

Rep. Mike Rogers, chairman of the House Permanent Select Committee on Intelligence, suggested the White House’s National Security Council Deputies Committee changed the report.

“That (committee) is populated by appointees from the administration,” Rogers said on NBC’s “Meet the Press.” “That’s where the narrative changed. The narrative was wrong and the intelligence was right.”

Georgia Sen. Saxby Chambliss, a Republican on the Senate Select Committee on Intelligence, thinks the National Security Council made the changes because all of the agencies that review the reports said at a Capitol Hill briefing that they did not.

“We had every leader of the intelligence community there,” the Georgia senator said on “Fox News Sunday.”  “The only entity that reviewed the talking points that was not there was the  White House.”

The attacks killed U.S. Ambassador Christopher Stevens and three other Americans.

Lieberman was joined on Fox by Georgia Sen. Saxby Chambliss, who said he expects Rice, the U.S. ambassador to the United Nations, and Secretary of State Hillary Clinton to testify before the Senate about the attacks on the U.S. Consulate and a nearby CIA annex.

Chambliss, the ranking Republican on the Senate Intelligence Committee, said Clinton has already agreed to testify and that Rice is "going to have to come in and testify at some point.”

Chambliss said a key question is what did President Obama or other top administration officials tell Rice to say.

The White House has defended Rice, saying she followed talking points based on the best available intelligence, with President Obama calling Republican-led attacks on her “outrageous.”

And on Saturday, the White House denied allegations about scrubbed terrorist involvement from original CIA talking points on the Libya attacks.

"The only edit that was made by the White House and also by the State Department was to change the word 'consulate' to the word 'diplomatic facility,' since the facility in Benghazi was not formally a consulate," said White House Deputy National Security Adviser Ben Rhodes.

"We were provided with points by the intelligence community that represented their assessment. The only edit made by the White House was the factual edit about how to refer to the facility," Rhodes also said.

His remarks came a day after Petraeus told House and Senate intelligence committees that the agency's original talking points suggested the attacks involved Al Qaeda affiliates and sympathizers – including the Libyan group Ansar al-Shariah.

On Sunday, Arizona Sen. John McCain again suggested that he would block a nomination of Rice for secretary of state.

“She has a lot of explaining to do. I’m curious about why she has not repudiated the remarks,” McCain, the ranking Republican on the Senate Armed Services Committee, said on CBS’ “Face the Nation. ” “I think we give all nominees the benefit of hearings. Maybe she could come back and say I was wrong. That would be a beginning. But under present circumstances, I don't think you could support any nominee right now.”

Rice purportedly was working off non-classified CIA talking points that had first been reviewed by the White House and other agencies including the Defense and State departments.

Republican Rep. Pete King told Fox on Saturday the next step is to learn who changed the talking points and why.

He also suggested the House Intelligence Committee could call Rice to testify.