WASHINGTON (AP) -- David Petraeus never shied away from the public eye before in times of crises. Now, he might not have a choice.
As details emerged about his extramarital affair with his biographer, Paula Broadwell, including a second woman who allegedly received threatening emails from the author, members of Congress said Sunday they want to know exactly when the now ex-CIA director and retired general popped up in the FBI inquiry, whether national security was compromised and why they weren't told sooner.
"We received no advanced notice. It was like a lightning bolt," said Democratic Sen. Dianne Feinstein of California, who heads the Senate Intelligence Committee.
Lawmakers also said it's possible that Petraeus will be asked to appear on Capitol Hill to testify about what he knew about the U.S. response to the Sept. 11 attack in on the U.S. Consulate in Benghazi, Libya, that killed four Americans, including the U.S. ambassador.
Rep. Peter King, chairman of the House Homeland Security Committee, said the circumstances of the FBI probe smacked of a cover-up by the White House.
"It seems this (the investigation) 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 General Petraeus was involved. It just doesn't add up," said King, R-N.Y.
Petraeus, 60, quit Friday after acknowledging an extramarital relationship. He has been married 38 years to Holly Petraeus, with whom he has two adult children, including a son who led an infantry platoon in Afghanistan as an Army lieutenant.
Broadwell, a 40-year-old graduate of the U.S. Military Academy and an Army Reserve officer, is married with two young sons.
Their affair will be the subject of meetings Wednesday involving congressional intelligence committee leaders, FBI deputy director Sean Joyce and CIA deputy director Michael Morell.
Petraeus had been scheduled to appear before the committees on Thursday to testify on what the CIA knew and what the agency told the White House before, during and after the attack in Benghazi. Republicans and some Democrats have questioned the U.S. response and protection of diplomats stationed overseas.
Morell was expected to testify in place of Petraeus, and lawmakers said he should have the answers to their questions. But Feinstein and others didn't rule out the possibility that Congress will compel Petraeus to testify about Benghazi at a later date, even though he's relinquished his job.
"I don't see how in the world you can find out what happened in Benghazi before, during and after the attack if General Petraeus doesn't testify," said Sen. Lindsey Graham, R-S.C.
Graham, a member of the Senate Armed Services Committee, wants to create a joint congressional committee to investigate the U.S. response to that attack.
Feinstein said she first learned of Petraeus' affair from the media late last week, and confirmed it in a phone call Friday with Petraeus. She eventually was briefed by the FBI and said so far there was no indication that national security was breached.
Still, Feinstein called the news "a heartbreak" for her personally and U.S. intelligence operations, and said she didn't understand why the FBI didn't give her a heads up as soon as Petraeus' name emerged in the investigation.
"We are very much able to keep things in a classified setting," she said. "At least if you know, you can begin to think and then to plan. And, of course, we have not had that opportunity."
The director of national intelligence, James Clapper, was told by the Justice Department of the Petraeus investigation on election night, and then called Petraeus and urged him to resign, according to a senior U.S. intelligence official who spoke on condition of anonymity because he was not authorized to discuss the investigation publicly.
FBI officials say the committees weren't informed until Friday, one official said, because the matter started as a criminal investigation into harassing emails sent by Broadwell to another woman.
The identity of the other woman and her connection with Broadwell were not immediately known, but that probe led agents to Broadwell's email, which uncovered the relationship with Petraeus, according to an official who spoke to The Associated Press on Saturday.
Concerned that the emails he exchanged with Broadwell raised the possibility of a security breach, the FBI brought the matter up with Petraeus directly, according to the official, who spoke on condition of anonymity because he was not authorized to publicly discuss the investigation.
Petraeus decided to quit, though he was breaking no laws by having an affair, officials said.
Feinstein said she has not been told the precise relationship between Petraeus and the woman who reported the harassing emails to the FBI. She said she has been told only that the woman was someone Petraeus "knew and was close to."
Georgia Sen. Saxby Chambliss, the top Republican on the Senate intelligence committee, called Petraeus "a great leader" who did right by stepping down and still deserves the nation's gratitude. He also didn't rule out calling Petraeus to testify on Benghazi at some point.
"He's trying to put his life back together right now and that's what he needs to focus on," Chambliss said.
King appeared on CNN's "State of the Union." Feinstein was on "Fox News Sunday," Graham spoke on CBS' "Face the Nation," and Chambliss was interviewed on ABC's "This Week."
Associated Press writers Michele Salcedo, Kim Dozier, Pete Yost and Adam Goldman contributed to this report.