“I think she deserves the ability and the opportunity to explain herself and her position,” Sen. John McCain told “Fox News Sunday.” ”But she’s not the problem. The problem is the president of the United States,” who, McCain said, misled the public on terrorist involvement.

Rice is widely seen as President Barack Obama’s top pick to replace Secretary of State Hillary Rodham Clinton, who is expected to step down soon, as the nation’s top diplomat. But Rice’s reputation took a serious hit this fall when she relied on unclassified talking points provided by the intelligence community that portrayed the Sept. 11 attack on the consulate in Benghazi, Libya, as a spontaneous assault by a mob angered by an anti-Muslim video posted on YouTube. The video was produced in the U.S.

Intelligence officials quickly amended their assessment to conclude the attack hadn’t been related to other film protests across the Middle East. But that revised narrative was slow to reach the public, prompting Republicans to allege a White House cover-up ahead of the Nov. 6 election.

The attack killed Ambassador Chris Stevens, a State Department computer specialist and two former Navy SEALs who were working as contract security guards.

McCain’s remarks were in contrast to his previous stance that Rice wasn’t qualified to replace Clinton, and that he would do “whatever is necessary” to block Rice’s possible nomination.

Obama responded to that by angrily challenging those who would block Rice’s nomination to take aim at him instead.

Sen. Lindsey Graham, McCain’s close friend and colleague on the Senate Armed Services Committee, told ABC’s “This Week” he still suspects the White House intentionally glossed over obvious terrorist links in the attack to keep voters from questioning Obama’s handling of national security.

But instead of repeating his prior assertion that he was “dead set” against a Rice promotion, Graham suggested he looked forward to hearing her out. If Rice were nominated, “there will be a lot of questions asked of her about this event and others,” said Graham.

The subtle shift in Republicans’ tenor on Rice could be the result of internal grumblings on how far to take party opposition. Democrats picked up extra Senate seats in the election to maintain their narrow majority, making it that much harder for the remaining 45 Republicans to block the president’s nominees.

One senior Republican Senate aide said Sunday that Republicans hadn’t united against Rice and were not convinced she was worth going after.

“There’s a definite sense within the caucus that you have to be conservative about where you put your firepower,” said the aide, who spoke on condition of anonymity because the official was not authorized to speak publicly on internal Republican deliberations. “The question is whether the caucus is prepared to filibuster her, and I’m not sure we were.”