The continued criticism of Ms. Rice, 48, a diplomat with close ties to Mr. Obama, deepens an already bitter and unusually personal feud between the White House and Republicans over Libya. Responding to a question about criticism of Ms. Rice at a news conference two weeks ago, Mr. Obama said, “If Senator McCain and Senator Graham and others want to go after somebody, they should go after me.”

It also raises the prospect of a confirmation battle if the president goes ahead with nominating Ms. Rice. To some extent, that battle is already under way, even before he has submitted her name. Ms. Rice’s visits to senators, which will continue Wednesday, bear all the hallmarks of a presidential nominee seeking to win over reluctant lawmakers.

A senior administration official said the harsh reaction to Ms. Rice’s appearance on Tuesday would have no effect on her chances for secretary of state. “They’ve been saying the same thing for months,” he said.

Senator John Kerry, Democrat of Massachusetts and the chairman of the Foreign Relations Committee, is the other leading candidate for the post. Several senators, including Mr. McCain, said they would prefer Mr. Kerry and predicted that he would sail through a confirmation hearing.

In a statement after the meeting, Ms. Rice said she incorrectly described the attack in Benghazi, which killed Ambassador J. Christopher Stevens and three other Americans, as a spontaneous protest gone awry rather than a premeditated terrorist attack. But she said she based her remarks on the intelligence then available — intelligence that changed over time.