The two Democrats are pitted against each other because California advances the top two vote-getters in a primary to the general election, regardless of their party.
In the presidential race, Romney began the campaign week with a speech that criticized the Obama administration for showing a lack of leadership around the globe, particularly in the Middle East.
And he chose to end it with a direct challenge to Biden's candor about the attack on the consulate in Benghazi, Libya.
"When the vice president of the United States directly contradicts the testimony, sworn testimony of State Department officials, American citizens have a right to know just what's going on," he said, referring to a hearing earlier in the week in a Republican-controlled House committee.
One official testified before the panel that he had been criticized for seeking additional security at the facility. A second said she personally had turned down requests for more protection at the facility in Benghazi.
Carney said, that despite Romney's allegation, there was no contradiction between what Biden said and what the congressional committee had been told.
"Requests for individual personnel at the thousands of facilities ... are not adjudicated at the White House," the spokesman said. "They are decided at the State Department."
Biden, campaigning in LaCrosse, Wis., did not mention Libya on the day after the debate. Instead, he mocked Ryan for having said on Thursday night that a House budget proposal that he authored would not lead to drastic spending cuts in Medicare, education and other areas.
"Congressman Ryan saying his budget does not have spending cuts is like Gov. Romney standing in an unemployment line and saying, 'I didn't outsource you job, I offshored it," he said, referring to a distinction Republicans sought to draw earlier in the campaign.
The controversy over Libya flared as both Romney and Obama looked ahead to their second debate, set for next Tuesday in Hempstead, N.Y.
After being accused by some Democrats of failing to prepare adequately for last week's encounter, Obama arranged for several days of rehearsals in Williamsburg, Va.
Romney was flying home to Massachusetts on Saturday so he, too, could get ready for an event likely to be watched by a television audience measured in the tens of millions.
The two men will hold their third and final debate on Oct. 22 in Boca Raton, Fla.
Espo reported from Washington. Associated Press writers John Flesher in Hudsonville, Mich., Michael Blood in Los Angeles, and Matthew Daly in LaCrosse, Wis. contributed to this report.
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