LIVE VIDEO: Benghazi Hearing

As lawmakers begin to look into the Benghazi attack, one person's testimony is most anticipated by congressional investigators probing the Sept. 11 attack on the U.S. Consulate in Libya: David Petraeus.

As lawmakers begin to look into the Benghazi attack, one person's testimony is most anticipated by congressional investigators probing the Sept. 11 attack on the U.S. Consulate in Libya: David Petraeus.

The former four-star general stepped down last week as CIA director because of an extramarital affair but has agreed to appear voluntarily before House and Senate investigative committees. Some members of Congress say Petraeus holds the answers to crucial questions about what happened in Libya.

Four GOP senators are demanding the White House open up to Congress about the attack that killed a U.S. ambassador and three other Americans.

"You and your senior administration officials have not been forthcoming in providing answers to the many questions that have emerged," wrote Sen. John McCain, R-Ariz., in a letter also signed by Sen. Lindsey Graham, R-S.C., Sen. Kelly Ayotte, R-N.H., and Sen. Ron Johnson, R-Wis.

"The American people and their representatives in Congress need to understand what you knew about the Benghazi terrorist attack and when you knew it."

Among the questions:

• When were officials in the Obama administration - including the president - made aware of the true nature of the attack that killed U.S. Ambassador to Libya Christopher Stevens and three others.

• Why did Obama administration members (U.N. Ambassador Susan Rice, Secretary of State Hillary Rodham Clinton, White House spokesman Jay Carney, and Petraeus) insist days after the killings that they arose out of a protest over an anti-Islam video outside the consulate that never happened?

• Who was aware that requests from the ambassador for more security forces were denied, and why were they denied?

• Why was a decision made not to send military assets from air bases to put down the attack given that the Pentagon and White House reportedly had real-time video of what was happening from a drone surveillance plane?

Four Senate and House committees are holding closed-door hearings this week on the Benghazi attack. Petraeus, now a civilian, has agreed to testify, said Sen. Dianne Feinstien, D-Calif., chairwoman of the Senate Intelligence Committee. He will appear before her committee Friday morning.

On Thursday, Senate and House intelligence committees will hear from acting CIA Director Michael Morell, National Intelligence Director James Clapper and others.

Petraeus' testimony would also be key to the Senate Armed Services Committee's investigation, McCain said.

"We'd want to ask him why there weren't significant forces there to respond" when the attack began and continued for more than seven hours, McCain said.

McCain and Sens. Graham and Ayotte are calling for a special inquiry into the Benghazi incident that would combine investigations currently spanning at least three Senate committees.

The senators said Petraeus should explain why he and other Obama administration officials for days after the attack publicly tied the attack to protests over an anti-Islam film even though the CIA station chief in Libya had reportedly informed superiors that the attack was a well-organized assault by known terrorists.

Then there is the issue of security levels in a dangerous region.

State Department security officials have testified that in the months preceding the attack, they monitored the growing presence of al-Qaeda-linked militias, and multiple attacks on U.S. and other Western diplomats in Benghazi, yet their requests for additional security were turned down by their superiors in Washington.

"Why was security at the consulate so inadequate despite two attacks on the consulate and attacks on British Embassy staff?" McCain said Wednesday. "Why did the president and other administration officials label the event in Benghazi a protest to 'a hateful video' ... when it was clear from the earliest hours that it was a sophisticated attack?"

Graham referred to news media reports that cited State Department sources alleging the U.S. presence in Benghazi was primarily a CIA operation under State Department cover, and that security was therefore CIA responsibility. But then why was the ambassador asking his superiors at State for more security, he said.

"If that was the deal, why didn't people on the ground know that?" Graham asked. "If you have these people in different rooms blaming each other this investigation is going to fall flat."

McCain said the investigation should also investigate the assertion by Petraeus' former mistress, Paula Broadwell, in a Colorado speech that the attack in Benghazi was launched to free detainees being held at the CIA annex there. The CIA denies any Libyans were being held at the compound.

"This person (Broadwell) who was associated with Gen. Petraeus said at some gathering (in Colorado) there were two or three Libyans in the CIA safe house. The CIA said that was patently false," McCain said. "We don't know and that's why we need an investigation."

For Petraeus, the hearings come at the worst possible time, said Elliott Abrams, senior fellow for Middle Eastern Studies at the Council on Foreign Relations. "He's doing this at a time of public humiliation."

Abrams, who was a government witness in the Iran-Contra hearings involving the Reagan administration, said Senate Democrats would have to agree to any joint investigation.

Abrams was convicted of withholding information from Congress and pardoned by President George H.W. Bush. He says a Senate hearing would not have to carry the threat of a criminal prosecution.

"Nobody's talking about charging anybody for anything more than having done a bad job or being incompetent," Abrams said. "It's in that sense less politically and emotionally charged."

Petraeus may also want to testify to vindicate his reputation, which has been tarnished by the affair and CIA involvement in Benghazi.

"It does offer him an opportunity to remind people that whatever the private problem here, we've lost a great public servant," Abrams said.