(Andrew Innerarity/Reuters)

Graham, interviewed on CBS’s “Face the Nation,” said he was “not going to promote somebody who I think has misled the country” over the Benghazi killing of U.S. Ambassador Chris Stevens “or is either incompetent. That’s my view of Susan Rice. There are other people out there.”

Graham, an influential senator on defense and foreign policy matters — perhaps not on the order of Sen. John McCain (R-Ariz.), but pretty close — said he thought “Susan Rice would have an incredibly difficult time getting through the Senate. I would not vote for her unless there’s a tremendous opening up of information explaining herself in a way she has not yet done.”

However, Graham stopped short of saying he would put a hold on or filibuster the nomination.

We’re hearing the White House was most displeased with Graham’s remarks and determined to fight for Rice’s confirmation should she get the nod.

Rice was giving the administration’s view of the situation at the time, her backers believe, and if another foreign policy official had appeared on the show, he or she would have said the same things.

In addition, the chatter is that President Obama really, really wants to nominate her.

The Washington Post is reporting that Obama is considering Sen. John F. Kerry (D-Mass.), the other State Department front-runner, to be defense secretary.

Speculators are beginning to muse about who would replace Rice at the United Nations, our colleague Colum Lynch reported last week.

The White House has begun considering at least two new candidates for the top U.N. job, including Samantha Power, who oversees U.N. policy at the White House, and Eileen Donahoe, the U.S. ambassador to the U.N. Human Rights Council, according to a source close to the Obama administration.