Boehner tried to take a less confrontational tone on Thursday, but nonetheless said the White House was refusing to make public e-mails and other documents he says show the political calculation behind the Rice TV appearance and other elements of the administration's Benghazi response.
"The White House continues to claim it only made stylistic changes to talking points used by Susan Rice, ignoring the fact that senior White House officials directed the changes being made" to those talking points, Boehner said.
Conservative media outlets also clearly see an opportunity to raise questions about Clinton that could be a factor in her 2016 calculations.
Respected conservative writer and commentator Terence Jeffrey reminded his readers this week of the initial Clinton Benghazi statement suggesting, "Some have sought to justify this vicious behavior as a response to inflammatory material posted on the internet."
Jeffrey said the State Department refuses to provide information about who told Clinton an Internet posting might be a possible cause.
Hicks told the hearing on Wednesday that U.S. diplomats in Libya reported back from the very beginning that they believed it was a terrorist attack.
Among the conservatives urging House Republicans to demand answers from Clinton directly is former Vice President Dick Cheney.
On Thursday, Cheney spoke to the weekly "Theme Team" meeting organized by House conservatives and two people present at the breakfast said the former vice president said if Clinton declined to voluntarily answer questions, then she should be subpoenaed to testify.
Another veteran of the George W. Bush administration also weighed in Thursday, in a way that highlights the intersection of Benghazi oversight and Benghazi politics.
In an e-mail sent to conservatives, former U.N. Ambassador John Bolton said, "What happened with Benghazi is not how it's supposed to be handled and I think it could be a hinge point for the Obama administration."
The Bolton note was distributed by the House GOP's campaign arm -- the National Republican Congressional Committee -- and asks for political contributions to the GOP. In fact, if you click on the links in that Bolton e-mail, it takes you to an NRCC fund-raising website that declares "Benghazi was a cover-up" over a photograph of Clinton and President Barack Obama.
That definitive assertion on a House GOP official fund-raising site is par for the course in Washington these days. But it gives Democrats fodder for their argument that Republicans have already made up their minds and aren't conducting oversight hearings with an open mind.
Clinton is now a private citizen. But close allies on the committee, including New York Democratic Rep. Carolyn Maloney, came to Clinton's defense during the proceedings. And other longtime Clinton political loyalists were privately nudging reporters and media outlets about the tone of the Benghazi coverage.
One veteran Democratic strategist, who spoke only on condition of anonymity because Clinton chafes at those who publicly speculate about her 2016 interest, noted her overwhelming popularity among Democrats.
"She will have to deal with this," the strategist said, "but it will not be central to the campaign."
Longtime Clinton ally and Democratic strategist Paul Begala takes a similar view.
"Once more, the GOP runs the risk of appearing to be blinded by their partisanship," Begala said. "I have no idea if Hillary will run. But I know this: If she does this issue will not be a major stumbling block."
Begala drew historical comparison -- between Clinton now and then-Vice President George H.W. Bush heading into the 1988 presidential campaign.
"Remember Iran-Contra?" Begala asked. "Infinitely more damaging than Benghazi. The Reagan administration sold weapons to the ayatollah's regime in Tehran, then diverted some of the proceeds to the (Nicaraguan) Contras, then lied about it. The scandal paralyzed the Reagan administration for 18 months."
There were high-level resignations and criminal convictions, Begala recalled.
"There was a major joint congressional investigation, with highly publicized, televised hearings. There was a special prosecutor. It was one of the biggest scandals of the 20th century. And two years later, it had no impact on Vice President Bush's campaign."