Obama administration officials held a closed-door, classified briefing on Wednesday in which they spent more than two hours detailing to senators the trade of five senior Taliban leaders for U.S. Army Sgt. Bowe Bergdahl, but many lawmakers decided to leave early.

Officials from the State Department, Pentagon and intelligence agencies showed senators a “proof of life” video taken of Bergdahl in captivity. The presentation also informed lawmakers that Congress wasn't informed of the exchange ahead of time as required by law, because the Taliban had threatened to kill Bergdahl if the deal was made public before it occurred.

But many senators found the video and the administration's case for urgency unsatisfactory, given claims that Bergdahl had deserted from a U.S. base in Afghanistan.

Sen. Saxby Chambliss (R-Ga.), ranking member on the Select Committee on Intelligence, appeared on Fox News to criticize the administration while the briefing was still underway.

"In fact, the briefing is still going on, but I don't see how anybody can walk out of there with any kind of comfortable feeling that the administration from a notification standpoint -- and I emphasize that -- did what they should have done or what they had the opportunity to do," he said. "I mean, it was like they didn't trust [Sen. Dianne Feinstein (D-Calif.)] and me. And, yet, the two of us knew about the bin Laden event for -- leading up to the takedown of bin Laden -- for months and months and months. And it's just very puzzling as to why they didn't notify anybody in Congress as to what was going on."

But Chambliss wasn't alone. NBC News host Chuck Todd noted on Twitter earlier Thursday that many senators decided to do the same.

"So many of my NBC colleagues are tracking down senators who were at classified briefing last night and many are admitting they left early," Todd said. "Amazing that so many senators from both parties didn't stay for the briefing until the end."

Sen. John McCain (R-Ariz.) stayed long enough to ask a question, but he walked out shortly after shouting at an official over an unsatisfactory answer, according to a Senate aide familiar with the process.

"I learned nothing," McCain told reporters afterward.

Sen. Rand Paul (R-Ky.), who criticized President Barack Obama for breaking the law, skipped the briefing entirely.