Republican presidential nominee Mitt Romney’s awkward debate moment Tuesday on the terrorist attack in Libya has not quelled Republican demands for more information about what the president knew, when he knew it and whether he should have anticipated the Sept. 11 event.

With the topic sure to come up again during Monday’s foreign policy debate, Romney will get another chance to make his case that the Obama administration failed to provide adequate security and only belatedly acknowledged that the deaths of four Americans, including U.S. Ambassador Chris Stevens, resulted from a terror attack rather than a violent protest.

Democrats cheered after President Barack Obama gave his strongest statement to date on the attack during Tuesday night’s debate, while Romney stumbled in his attempt to put the president on the defensive. But the administration has not provided a full account of what the White House knew about the deteriorating situation in Benghazi prior to Sept. 11, why it took the administration weeks to shift from the initial story that the attack was a response to an anti-Islam YouTube video and who rejected requests for additional  security at the U.S. mission.

Republicans in Congress are not about to let the issue go,  with several committee investigations under way.

Sen. Kelly Ayotte (R-N.H.), a top Romney surrogate, said the president wants to make it seem like he was on top of what happened, when the reality is he and his administration were talking about the YouTube video for weeks.

“I think there are still very serious questions,” she said Wednesday. “The question he did not answer at all last night was, ‘Were you aware of the prior attacks on this consulate, including the one in June, when a hole was blown in the wall?’ If he didn’t know, why? Why were the security requests denied in light of the security situation that was clearly getting worse? It really begs the question of what did he know.”

On Tuesday, before Romney and Obama squared off, Sen. Lindsey Graham (R) sent letters to top intelligence officials asking if the president was told about attacks on the consulate in April and June.

“Did you inform the president of these attacks? If so, what action was taken to protect our consulate? If you did not inform the president, why not?” the South Carolina lawmaker asked.

Sen. Bob Corker (R-Tenn.), a senior Republican on the Senate Foreign Relations Committee, noted Obama’s efforts to capitalize politically on his record on terrorism.

“In fairness, one of the reasons the administration has responded the way they have responded is they have spiked the ball so many times on Osama bin Laden,” he said.

But Corker acknowledged that the scrutiny being applied by Republicans “no doubt has been heightened by when it happened” — in the fall of a tight presidential election campaign.

“Americans are not satisfied with the changing story and remaining questions surrounding Libya,” Romney spokesman Ryan Williams said. “The president and his administration have repeatedly misled the public.”

On Tuesday night, Romney charged that Obama was reluctant to recognize the Benghazi attack as terrorism. Obama said he did so almost immediately in a Rose Garden statement.

Debate moderator Candy Crowley backed up Obama’s position, creating an awkward moment for Romney. That allowed the president, for the first time after weeks of playing defense on the issue, to shift to offense and rip Romney for politicizing the issue, while also taking responsibility for the security failure and vowing once again to hunt down the killers.  

In fact, what Obama said in his Rose Garden response to the deaths in Libya was: “No acts of terror will ever shake the resolve of this great nation.” The Romney campaign charged that Obama’s statement was generic and said that his administration, when asked repeatedly for days afterward if the Benghazi attack was terrorism, would not say it was.

“Gov. Romney was right on the facts and he’ll continue to highlight the ever-changing story,” Williams said. “Anybody who followed this topic understood the Obama administration falsely maintained that this was a spontaneous reaction to a YouTube video.”

But Obama’s campaign and surrogates pointed to the president’s use of the word “terror” three times in the two days following the attack and accused the Romney camp of playing politics with national security.

White House Press Secretary Jay Carney said Wednesday that Obama believed it was a terror attack, even though the intelligence at the time indicated that it appeared to stem from the video. Carney told reporters the attack could be both a result of a protest and an act of terror.

Sen. John Kerry (D-Mass.), chairman of the Foreign Relations Committee and the stand-in for Romney in the president’s debate preparations, dismissed Romney’s attacks as fumbling and unpresidential.

“The president called it an act of terror,” Kerry said on MSNBC’s “Morning Joe.” “You don’t play games with national security. … Before anybody knew the facts, Mitt Romney was politicizing this issue.”

Still, Kerry said that Congress will continue its inquiries. “We want the facts and we’ll get the facts,” he said.

Investigations continue on both sides of the Capitol, including probes by Kerry’s committee, the Senate Intelligence Committee chaired by Sen. Dianne Feinstein (D-Calif.), and the Senate Homeland Security and Governmental Affairs Committee, led by Chairman Joe Lieberman (I-Conn.) and ranking member Susan Collins (R-Maine).

House Oversight and Government Reform Chairman Darrell Issa (R-Calif.)  held a hearing last week, during which State Department officials acknowledged that the agency denied requests for more security in Tripoli. “The warning signs were there and they weren’t heeded,” Issa said Sunday on CBS.

Both Issa and Corker said Congress should focus after the elections on longterm issues surrounding American diplomacy in tumultuous parts of the world, rather than on the back-and-forth over who said what when.

Indeed, once the political nature of the dispute is resolved on Nov. 6, the focus in Congress is likely to shift.

Particularly salient to Corker are questions surrounding the expeditionary roles American diplomats have assumed in places such as Benghazi.

“When you’re operating in that kind of environment, there should be some policies and procedures that are very different than what you have when you’re operating” in more standard diplomatic posts, he said.

Emily Cadei contributed to this report.