The Capitol Hill news conference inevitably led to questions about Rice, and the lawmakers made clear they would oppose her selection.
"We will do whatever is necessary to block the nomination that's within our power as far as Susan Rice is concerned," said McCain, the top GOP senator on the Armed Services Committee and Obama's presidential rival in 2008.
Graham, who said last weekend that he would oppose her nomination, said Rice "is so disconnected from reality that I don't trust her. And the reason I don't trust her is because I think she knew better, and if she didn't know better then she shouldn't be the voice of America. Somebody has got to be paying a price around this place."
Republican Sen. Jim Inhofe of Oklahoma, who is poised to replace McCain as the top Republican on Armed Services, said in a statement that Rice "would not be a fitting replacement at the State Department should Secretary Clinton step down."
"During her time as the U.S. ambassador to the United Nations, Rice has been the Obama administration's point person in pursuing liberal causes that threaten U.S. sovereignty," Inhofe said.
More disconcerting for Rice's prospects was the unease expressed by Collins, who is also a member of the Armed Services panel and the top Republican on the Homeland Security committee.
"I would need to have clear answers from Ambassador Rice before I could support her for any position," Collins told reporters. "She has a lot of explaining to do. She has yet to come forward and explain why she gave the misleading information to the American public. And we don't have the answer to that yet. I would need the answers before I would be prepared to confirm her for any position."
Another name mentioned as a possible candidate for the top job at the State Department is Senate Foreign Relations Committee Chairman John Kerry, D-Mass., who has taken on envoy roles for the administration in Afghanistan and had been mentioned for the post when Obama was first elected.
Senior Senate aides and lawmakers have said Kerry would have no problem winning Senate confirmation and see him as a far better fit than Rice, who has had little contact with members of Congress. But the selection of Kerry would create an opening for the Senate seat in Massachusetts, and Republican Sen. Scott Brown, who lost re-election last week, would be a heavy favorite to win the seat.