The Washington Post’s Bob Woodward predicted Sunday on NBC’s Meet the Press that the David Petraeus saga won’t go away anytime soon, especially since the former CIA director was on the ground in Benghazi just before the election conducting his own investigation.

Of the affair between Petraeus and his 20-years-junior married biographer, Woodward said he’s heard Petraeus was “obviously … enchanted with her.”

“Interestingly enough I think the David Petraeus story is not going away. Just this coming week there are going to be hearings in the House in the intelligence committees on the Benghazi episode a month ago where four Americans including the ambassador were killed,” Woodward said.

The House and Senate Intelligence committees hold their closed-door hearings on Thursday. The same day, the House Foreign Affairs Committee holds its own open hearing, to which Secretary of State Hillary Clinton turned down an invitation to testify.

“It turns out that Petraeus a week and a half ago went to Tripoli, Libya, and conducted his own personal inquiry into Benghazi, interviewed the station chief, actually got the base chief from Benghazi down, interviewed him,” Woodward said. “Interviewed the head I think twice of the quick reaction force that was involved in this episode.”

“So he knows the full story. He has a lot of credibility with Republicans, who as we know are on fire about Benghazi. And now the acting CIA Director, Mike Morrell, is going to have to present that evidence.”

Petraeus can still be subpoenaed to testify as a private citizen, but the GOP vice-chairman of the Senate Intelligence Committee indicated yesterday that the four-star general would need time to try “to put his life back together.”

Woodward predicted, though, that Petreaus’ version of the Benghazi attack “would essentially back up the White House” — but with a potential surprise.

“And there are still unanswered questions and so forth. But one of the things Petraeus always did was dig deep. And so he — apparently there are videos and there are tapes or tapes and pictures and things that can be shown,” he said.

“So it is not going away. And the question will be I suspect will he be asked to testify as a private citizen either informally, in closed door and so forth. Probably only Petraeus can — if he has the data — stop this Benghazi frenzy.”

Sen. Tom Coburn (R-Okla.) said that resignation or not, Petraeus still needs to answer Benghazi questions.

“He was obviously the person in charge of the CIA and he has information that probably other people don’t have,” Coburn said. “So I think it’s still going to be important that his input comes into the conclusion and what we find about what went wrong — were made. We obviously weren’t prepared. I think you have to spend time to find out what happened and how it happened.”

Sen. Chuck Schumer (D-N.Y.) said lawmakers should first see if Acting Director Mike Morell, who will testify in Petraeus’ place, can supply the information from the general’s fact-finding mission, “and then we should take it from there.”