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He also said Mr. Obama deferred to him and to Chairman of the Joint Chiefs of Staff Gen. Martin E. Dempsey.

A hold is a debate technique, signaling Mr. Graham intends to slow the nomination. Unless he relents, Democrats will likely have to muster 60 votes in order to cut off debate and move to a final up-or-down vote on the nominees.

Democrats wasted no time in pouncing on Mr. Graham’s vow to hold up important White House nominations.

“This is unprecedented, unwarranted to stop or attempt to stop the nominations of the secretary of defense and the CIA director. The men and women of the Department of Defense need a secretary of defense,” said Sen. Jack Reed, Rhode Island Democrat, also appearing on “Face the Nation” on Sunday morning.

“The idea that the president was not engaged [as the Benghazi attacks unfolded] is, I think, completely wrong,” he added.

While he plans to halt the confirmations of Mr. Brennan and Mr. Hagel, Mr. Graham said he will not lead a filibuster against them. Other Republicans harbor deep reservations about Mr. Hagel, but also oppose a filibuster.

During an appearance on “Fox News Sunday,” Sen. John McCain, Arizona Republican, said he still has “grave concerns” about Mr. Hagel and that, at this point, he’s leaning toward voting “no” on his nomination.

“I will see the rest of the answers to his questions, but certainly I have very grave concerns,” he said.

Those concerns, however, are not enough for Mr. McCain to take part in a filibuster, arguing that the president’s picks deserve a fair up-or-down vote in the Senate.

“We have never filibustered a presidential Cabinet appointee, and I don’t think we should start here, he said. “Elections have consequences, unfortunately.”

Sen. Richard J. Durbin, Illinois Democrat, predicted that Mr. Hagel ultimately will be confirmed.

“Republican senators have told me privately they are not going to initiate the first filibuster in history on a secretary of defense nominee,” he said on NBC’s “Meet the Press.”