Graham, R-S.C., and McCain, R-Ariz., also threatened to filibuster the nomination of Jeh Johnson for homeland security secretary and a host of other presidential picks unless the Obama administration releases more information about the Sept. 11, 2012, assault on the U.S. diplomatic mission and lets survivors talk to congressional lawmakers.
The attack by al-Qaida-linked militants killed four Americans, including Ambassador Christopher Stevens, and injured 10 others.
No one has been arrested, although an indictment was filed against one suspect in August.
Republicans say the attacks show severe security lapses that cannot be ignored.
Some accuse the White House and State Department of a coverup to protect President Barack Obama during his re-election campaign and Hillary Clinton, who was secretary of state at the time and is widely considered a leading 2016 Democratic presidential hopeful.
"What I am asking for is to talk to the people who were there," Graham said at a Capitol Hill news conference.
Graham and McCain said they would try to filibuster not because they questioned the nominees' merits but rather because they wanted to extract concessions from the Obama administration.
"That is the only leverage we have," Graham told reporters.
"That's the only way we get their attention," McCain told The Wall Street Journal.
Both senators said they would likely vote for the nominees.
Johnson is "a really well-qualified guy," Graham said.
But McCain told reporters, "You cannot look at this issue without remembering it was in the midst of a presidential campaign."
He referred to Clinton as the "presumed Democratic nominee for president in 2016."
The White House has acknowledged security failures in Benghazi and said administration officials have testified at 13 congressional hearings, participated in 40 staff briefings and provided more than 25,000 pages of documents.
It also said a diplomatic security agent who survived the attack testified before the House Oversight and Government Reform Committee.
But the State Department told Graham in a letter it was concerned additional congressional interviews could jeopardize a criminal trial in which the survivors could be witnesses.
"Additional interviews outside of the criminal justice process could jeopardize the success of a criminal case by prematurely alerting individuals who may be charged about the details of government's case against them -- possibly leading to attempts to thwart the investigation," a department official told Politico.
McCain, Graham and other Republicans dismissed that argument, saying the interviews would not jeopardize the government's case.
In a filibuster, a senator or series of senators tries to delay or prevent a vote by talking for as long as they wish and on any topic they choose. The filibuster can be overridden by at least 60 senators voting to end the debate.
Last week Sen. Rand Paul, R-Ky., said he would put a hold on Yellen's nomination as Fed chairwoman unless the Senate voted on his bill to increase congressional scrutiny of the central bank, created by Congress in response to a series of financial panics 100 years ago.
A filibuster can be avoided in the first place if at least 60 senators support Yellen or Johnson in a procedural vote. A simple majority of 51 senators would then be needed to approve the nomination.
Fifty-five senators are in the Democratic Caucus, including Cory Booker, D-N.J., who is to be sworn in as a senator Thursday. The Republican Caucus has 45 members.
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