Sen. James Inhofe, R-Okla., said last week impeachment was possible over the "most egregious cover-up in American history.
"People may be starting to use the I-word before too long," Inhofe told radio host Rusty Humphries, according to The Hill.
"The I-word meaning impeachment?" Humphries asked.
"Yeah," Inhofe responded.
Former Arkansas governor and one-time presidential candidate Mike Huckabee, too, chimed in his radio show that Obama will not serve out his full second term because of his complicity in a cover-up with Benghazi.
At issue is essentially a game of who knew what when.
While Obama called the incident an "act of terror," his administration initially blamed the release of an anti-Muslim video for a spontaneous rally outside the consulate. Witnesses testified last week that they knew it was a terrorist attack and that the diplomatic mission was denied more security when requested.
Obama said Monday that Republicans' concern with the administration's first talking points about the attack is a "sideshow" and that a top-level review was completed and its recommendations are being implemented.
"We've got a whole bunch of people in the State Department who consistently say, 'you know what, I'm willing to step up, I'm willing to put myself in harm's way because I think that this mission is important in terms of serving the United States and advancing our interests around the globe,' " Obama said during a news conference with British Prime Minister David Cameron. "And so we dishonor them when we turn things like this into a political circus."
Obama chided the GOP for trying to "spin" the American deaths.
"We don't have time to be playing these kinds of political games here in Washington," Obama said. "We should be focused on what are we doing to protect them."
Chaffetz, the chairman of a House subcommittee overseeing foreign operations, flew to Tripoli, Libya, to interview key players in the American embassy, and says the administration has misled Americans.
"Amen," Chaffetz said in response to Obama's comments. "It's high time that the president stopped politicizing this."