Senate Majority Leader Harry Reid, D-Nev., said the emails "prove there simply was no cover-up."
"Yet Republicans, with full knowledge of these emails, claimed the White House was hiding the truth," Reid said.
House Minority Leader Nancy Pelosi, D-Calif., agreed with Obama that the GOP focus was a "sideshow."
Yet Republicans made clear they have no plans to back down, with Boehner telling reporters that the GOP members on five committees were "working overtime" on the Benghazi issue.
Eight months after the attack, the issue remains a political winner with the Republican base as conservatives have been ferocious in assailing Obama. Rank-and-file GOP members and outside groups have pressured Boehner to appoint a special select committee to investigate. Instead, Republicans are pursuing their own inquiries and promising to call more witnesses to testify publicly, including the veteran diplomat and retired admiral, Thomas Pickering, who led an independent review of the attack that widely criticized the State Department's insufficient security at the facility.
Pickering and former Joint Chiefs Chairman Mike Mullen sent a letter Thursday to the House oversight committee chairman saying they will testify in public but not submit to private interviews with staff investigators prior to their testimony.
"The public deserves to hear your questions and answers," Pickering and Mullen told Rep. Darrell Issa, R-Calif. They offered to appear before the panel either May 28 or June 3.
The emails disclosed on Wednesday underscored the turf battle between the State Department and CIA, as neither wanted to take the blame for the attack. They also showed the reluctance within the administration about saying anything definitively as officials scrambled to write talking points for lawmakers and U.N. Ambassador Susan Rice, who discussed the attack on Sunday talk shows.
Rice's widely debunked remarks that cited protests over an anti-Islam video as the cause of the attack fueled the criticism of the administration and later cost her a chance at becoming secretary of state.
A senior U.S. intelligence official, speaking on a condition of anonymity without authorization to discuss the matter on the record, said CIA deputy director Mike Morell edited the talking points after a meeting at the White House on Saturday, Sept. 15. The White House document release showed Morell's hand-written notes, scratching out from the CIA's early drafts mentions of al-Qaida, the experience of fighters in Libya, Islamic extremists and a warning to the Cairo embassy on the eve of the attacks of calls for a demonstration and break-in by jihadists.
The emails show that Morell's boss, then-CIA Director David Petraeus, apparently was displeased by the removal of so much of the material his analysts had proposed for release. "Frankly, I'd just as soon not use this, then," Petraeus wrote after receiving Morell's edited version.