Rep. Peter King reiterated Sunday that General David Petraeus, who stepped down as head of the CIA following revelations of an extramarital affair, will very soon have to answer congressional questions about the Obama administration's handling of the Sept. 11 terror attack in Benghazi, Libya.

"My strong recommendation is Gen. Petreaus has to testify," the New York congressman told Fox News. "We can’t find out what happened in Benghazi unless David Petreaus testifies. He was at the center of it all. He is an absolutely essential witness."

King questioned the timeline of the FBI’s investigation into personal emails of Petraeus, and when high-ranking government officials, including the president, were made aware that the then CIA director was being investigated.

“It seems this has been going on for several months and yet now it appears that they’re saying that the FBI didn’t realize until Election Day that Gen. Petraeus was involved. It just doesn’t add up,” King also said Sunday on CNN’s “State of the Union.”

“In this type of investigation, with the FBI investigating emails, the emails leading to the CIA director, and it taking four months to say the CIA director was involved. So, I have real questions about this. I think a timeline has to be looked at and analyzed to see what happened.”

With such a high ranking official being investigated, King said the president, or at least his national security advisor, should have been alerted at the earliest stage of the investigation.

He added that while Petraeus was an outstanding general and public servant, "nobody is irreplaceable in government.” King, however, predicted that in the "short term any time you lose someone of Gen Petraeus stature, especially under these circumstances, it does create at least a short-term gap. But again, there are other people there who can and will definitely fill in.”

King said he expected hearings to be held this week into the situation at the same time members of Congress begin working on a deal to avoid the looming fiscal cliff, which King expects will result in a compromise coming between both parties in Congress and the president.

U.S. Ambassador Chris Stevens was killed on Sept. 11 alongside three other Americans, when the Benghazi consulate was attacked.

In his letter of resignation, Petraeus cited an extramarital affair he had been having. “After being married for over 37 years, I showed extremely poor judgment by engaging in an extramarital affair,” Petraeus said in his letter to President Obama. “Such behavior is unacceptable, both as a husband and as the leader of an organization such as ours.”

Petraeus, who had a distinguished military career, revealed no additional details. However, an FBI source says the investigation began when American intelligence mistook an email Petraeus had sent to his girlfriend as a reference to corruption. Petraeus was commander of U.S. Forces in Afghanistan from July 4, 2010 until July 18, 2011.

Petraeus decided to quit, though he was breaking no laws by having an affair, officials said.

"He decided he needed to come clean with the American people," said Steve Boylan, a retired army officer and former Petraeus spokesman who talked with him Saturday.

In a phone call, Petraeus lamented the damage he'd done to his "wonderful family" and the hurt he'd caused his wife, Boylan said. Petraeus has been married for 38 years to Holly Petraeus.

"He screwed up, he knows he screwed up, now he's got to try to get past this with his family and heal," said Boylan.

The investigation began last spring, but the FBI then pored over his emails when he was stationed in Afghanistan.

The woman who was having an affair with Petraeus is a journalist who had been writing about him.She interviewed the general and his close associates intensively for more than a year to produce the best-selling biography, "All In: The Education of General David Petraeus," which was written with Vernon Loeb, a Washington Post editor, and published in January.

She is married with two young sons and has not responded to multiple emails and phone messages. She'd planned to celebrate her 40th birthday in Washington this weekend, with many reporters invited. Her husband emailed guests to cancel the party.

CIA officers long had expressed concern about her unprecedented access to the director. She frequently visited the spy agency's headquarters in Langley, Va., to meet Petraeus in his office, accompanied him on morning runs around the CIA grounds and often attended public functions as his guest, according to two former intelligence officials

Republicans, including King, contend that the general's resignation should not preclude him from speaking to House and Senate committees looking into the Obama administration's handling of the Sept. 11 attacks.

The acting director of the CIA, Mike Morell, is expected to take the general's place at the closed door intelligence committee hearings set for Thursday on Capitol Hill.

Still, the White House, with concurrence by the FBI and Justice Department, held off on asking for Petraeus’ resignation until after the election. His resignation occurred three days after the election, avoiding the possibility that Obama’s ill-fated appointment of Petraeus could become an issue in the election.

FBI agents on the case were aware that such a decision had been made to hold off on forcing him out until after the election and were outraged.

King also said Sunday that House Speaker John Boehner has offered enough in spending reductions and ways to increase revenue to the federal government that would not require increasing taxes for Democrats and Republicans to make a deal to avoid the fiscal cliff.

Rebutting the idea that President Obama received a mandate in last week’s election to raise taxes, King said the only real mandate anybody in Washington had from voters is to get a deal done.

He said that Boehner has put enough on the table for a deal to be reached.

“Republicans feel strongly that tax rates should not be increased,” King said. “Speaker Boehner has shown his willingness to work out an agreement here that could be done by affecting deductions and loopholes in the upper tax bracket so that the president would get the revenue that he said [during the election] he’s looking for, but it would be done in a way that tax rates are not increased, so therefore we would not slow economic growth. If both sides want an agreement, I think John Boehner has put enough on the table that an agreement can be reached.”

The Associated Press contributed to this report.