The increasingly bizarre sex scandal that cost CIA Director David Petraeus his job will likely dominate President Obama's first White House press conference in months on Wednesday, an occasion the president had hoped to use to push his policies on the looming fiscal cliff crisis.

Administration officials Tuesday framed the affair between Petraeus and his biographer, Paula Broadwell -- and possible improper behavior between Gen. John Allen and a woman threatened by Broadwell -- as an isolated event that should not distract leaders from the big issues that both the White House and Congress must resolve before year's end.

But Obama will be hard-pressed to downplay a story that has consumed Washington and shows no signs of losing momentum.

"It's a headache for a president who has just been re-elected and wants to lay out his priorities," said Republican strategist Ron Bonjean. "But his priorities aren't going to be the story. It will be his reaction to Petraeus and Allen. You might as well consider this a lost week for him."

The FBI investigation that forced Petraeus to resign last week expanded Tuesday to Allen, the commander of U.S. and NATO troops in Afghanistan. Allen's confirmation as the new NATO chief for Europe has been put on hold as authorities examine thousands of pages of communications between the general and Tampa, Fla., socialite Jill Kelley, who reported harassing emails from Broadwell that ultimately toppled Petraeus.

Allen claims his relationship with Kelley was platonic and that the emails were entirely appropriate, according to aides of the general.

Thus far, the president has kept his distance from the scandal. When Petraeus swiftly resigned, that initially protected the White House from political damage. However, the episode did raise the profile of another story in which the CIA played a role -- the Sept. 11 attacks in Benghazi, Libya, which killed U.S. Ambassador to Libya Christopher Stevens and three other Americans.

"The timing of the Petraeus resignation brought [Benghazi] back front and center," said Victoria Coates, former foreign policy adviser for Texas Gov. Rick Perry and adjunct fellow at the Foundation for Defense of Democracies. "If would be healthy for the public if the president clarified what happened there."

Petraeus will not testify on Capitol Hill as originally planned, even though the CIA was responsible for security at the U.S. consulate in Benghazi. When asked if Petraeus should appear before lawmakers, White House press secretary Jay Carney on Tuesday said the decision was "up to Congress."

Obama, who rarely holds news conferences, had planned on using his bully pulpit to press for a series of tax increases and spending cuts he contends are the best path to avoid the so-called fiscal cliff. And some analysts said the Petraeus affair wouldn't entirely overshadow that.

"I don't think this incident means there is a broader crisis in the intelligence and military communities," said Jordan Tama, a professor at American University and intelligence and counterterrorism policy adviser to Obama's 2008 presidential campaign. "It's unfortunate, but the public can separate Obama from what happened. He'll still be able to deliver his message."