Gohmert, a former Texas state judge, used a legal analogy to make his point.
"If one party to a question or dispute has evidence that either it refuses to produce or it has destroyed while it was in its possession, then the jury, the fact-finders, may consider as evidence that what evidence they had and refused to produce was against their position that they were espousing," he said. "That's true in courts, and I think it may have some application here. ... We're about to the point where we're going to just have to take it as a fact that the evidence they're refusing to produce hurts what they say happened in Benghazi and supports the worst of our fears about what this administration failed to do."
What are those worst fears? Former Rep. Allen West (R-FL), who joined Gohmert at the press conference, pointed to theories advanced by conspiracy web sites like InfoWars and World Net Daily: The CIA was helping transfer arms from Libyan rebels to Syrian rebels and that could explain what motivated the attack that killed U.S. ambassador Chris Stevens and others.
"The simple question that has to be answered is: Why was Ambassador Chris Stevens in Benghazi, Libya, in the heart of radical Islamist territory, on 9/11, being guarded by Islamic militias? Now that's a start," West told reporters. "Is it true that we were running guns? The ambassador was meeting with a representative from Turkey. We know that Turkey is behind the Islamist forces (in Libya). Were they talking about getting guns that we provided to the rebels there, who turned out to be al-Qaeda, Muslim Brotherhood-backed, and then getting them up into Turkey to come down into Syria. Now today we have al-Qaeda and the Muslim Brotherhood training Islamist fighters in Libya to go to Syria."
Gohmert and West were drawing attention to a letter sent Tuesday to House Speaker John Boehner. The letter, signed by former national security officials and printed on the letterhead of the conservative Center for Security Policy, urged Boehner to form a select House committee to investigate the Benghazi attacks.
Boehner, for his part, also criticized the White House for failing to answer Republican questions about Benghazi in a Wednesday statement.
"For the past year, this administration has failed to provide sufficient answers, fully comply with subpoenas, and make available relevant individuals to provide testimony. In short, this administration hasn't been upfront with the American people or this Congress," he said. "Republicans will not stop until we get to the truth. We will press forward with our investigation until we have answers, full accountability, and justice."
Other conservative lawmakers reapplied pressure on the White House on the one-year anniversary of the Benghazi attacks. Rep. Darrell Issa (R-CA) announced a House Oversight Committee hearing would be held next Thursday to receive testimony from State Department-appointed officials who were charged with investigating the attack. The day before, Issa sent a letter to Kerry demanding that he make eyewitnesses to the attack available to the committee.
Sen. Marco Rubio (R-FL) penned a Fox News editorial that chastised the White House and Senate Democrats for failing to provide answers on the attack. In his own statement, Sen. Lindsay Graham -- after recollecting his own experience during the 2001 attack -- pledged to keep pushing for answers from the White House on Benghazi.
"Questions about what happened in Benghazi remain unanswered and the American people deserve answers," Graham said. "But most of all, we owe it to the victims' families. I have met many of them, and I will not stop pushing for accountability and for answers so I can look them in the eye and tell them the truth about what happened."