Hagel, 66, who served two terms in the Senate, has faced challenges from members of his own party because of his past opposition to unilateral sanctions against Iran, his comment in 2006 about the influence of what he once called "the Jewish lobby," and his statements against the U.S. troop buildup in 2007 that hastened the end of the Iraq war.
Even as McCain predicted Hagel's confirmation, Republican Senator Lindsey Graham of South Carolina stepped up his criticism of the nominee.
"You're talking about a person whose voting record shows softness on Iran and antagonism toward Israel beyond belief," Graham said on the "Fox News Sunday" program. "He'd be the most antagonistic senator toward the state of Israel in history."
Graham, who also serves on the Armed Services Committee, said on Feb. 11 that he would block confirmation votes for Hagel and for John Brennan, President Barack Obama's choice to head the Central Intelligence Agency, until receiving more detailed information about the Benghazi attack, which left four people dead, including U.S. Ambassador Christopher Stevens.
McCain said there were still unanswered questions about what the president did the night of the attack, as well as why then-Secretary of State Hillary Clinton wasn't aware of how vulnerable the mission was.
Speaking today on NBC's "Meet the Press," one of three Sunday news shows on which he appeared, the new White House chief of staff, Denis McDonough, expressed confidence that the dispute over Benghazi would be resolved soon. The administration has already sent detailed written responses to lawmakers' questions, he said. In addition, there have been 20 congressional briefings, he said, and more than 10,000 pages of documents have been provided.
"The president is not done with Benghazi," McDonough said. "He's demanded of us, since that night, to find out exactly what happened, and to make every reform needed to ensure it does not happen again."
On another Obama priority, gun control, McCain said that legislation requiring universal background checks backed by Senators Tom Coburn, an Oklahoma Republican, and Joe Manchin, a West Virginia Democrat, may gain enough support in the Senate to pass.
Their proposal is intended to close the so-called gun-show loophole. Under current law, purchases at such shows currently don't fall under requirements for checks of criminal records or mental-health histories.
"I applaud their efforts," McCain said. "We want to do everything we can to prevent guns from falling into the hands of people who are mentally unbalanced or criminals."
With assistance from William Selway in Washington. Editors: Leslie Hoffecker, Ann Hughey
To contact the reporters on this story: Jeff Plungis in Washington at jplungisbloomberg.net; Elliot Blair Smith in Washington at esmith29bloomberg.net
To contact the editor responsible for this story: Steven Komarow at skomarow1bloomberg.net