Senator John McCain, R-Ariz., said after the meeting he was left with more questions than answers. "We are significantly troubled by many of the answers we got and some that we didn't get," McCain said Tuesday.
"All I can tell you is that the concerns I have are greater today than they were before and we're not even close to getting the basic answers."
Their criticism centers around Rice's comments five days after the Benghazi attacks on several Sunday political talk shows where she said the assault on the U.S. Consulate appeared to be "spontaneous" and not "premeditated" -- statements that proved to be untrue.
In a statement after yesterday's meetings, Rice said, "[W]hile we certainly wish that we had had perfect information just days after the terrorist attack... the intelligence assessment has evolved."
An afternoon meeting with Sen. Joe Lieberman, I-Conn., went far better. "I felt that she was telling me the truth, the whole truth and nothing but the truth," he said.
But in the Senate where a single member can block a nominee's confirmation, Lieberman's support may not be good enough.
Sen. Kelly Ayotte, R-N.H., told CBS News she will put on a hold for Rice's potential nomination "for now."
"There are still additional follow-up questions that we will have," she said.
The White House, meanwhile, insists Rice has shared all she can. "I would simply say that there are no unanswered questions about Ambassador Rice's appearances on Sunday shows," White House spokesman Jay Carney said.
that the administration thinks the Republicans "can never be satisfied" regardless of what Rice says.
"They're targeting rice as a proxy for the administration," Dickerson said of Rice's critics. But he added that they do have questions, including if her explanation "was this a result of an effort to massage the story because we were in an election year or was this just the fog of the moment?" Dickerson said Rice's critics want to know.