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He also said Mr. Ryan’s own budget that he wrote as chairman of the House Budget Committee would have spent $300 million less on embassy security than Mr. Obama wanted. However, at a hearing earlier this week, Deputy Assistant Secretary of State Charlene Lamb told a House panel that security decisions in Libya were not related to budget issues.

Ahead of the 90-minute debate, the Obama camp had tried to create a narrative that Mr. Ryan and Mr. Romney are lying about their record.

“We now know that Mitt Romney will say anything to win, even if it’s not true,” Obama campaign manager Jim Messina told reporters earlier in the day. “The question now is whether Congressman Ryan will adopt the same dishonest strategy, or if he’ll stand by the very extreme positions he’s taken as the intellectual leader of the Republican Party.”

After the debate, Mr. Obama said he was “going to make a special point of saying that I thought Joe Biden was terrific tonight. I could not be prouder of him.”

Mr. Romney’s team has countered that it’s Mr. Obama who is obfuscating things, accusing him of lying when he says the Republican has a $5 trillion tax-cut plan.

Last week’s presidential debate reversed the fortunes of both candidates, as the challenger drew rave reviews, and Mr. Obama has spent the week since explaining away his performance. Mr. Romney’s backers were re-energized, while many in Mr. Obama’s camp have been wringing their hands.

The latest Real Clear Politics average of national polls showed Mr. Romney with a razor-thin edge nationally. And the latest The Washington Times/Zogby Poll this week found voters now give Mr. Romney the upper hand when it comes to national security issues and restored Mr. Romney’s lead when it comes to which candidate they trust on the economy and jobs.

Mr. Obama has acknowledged he “had a bad night.” The blow, though, was softened by a better than expected jobs report released last week that said the national unemployment rate had dropped from 8.1 percent to 7.8 percent — returning it to the level that Mr. Obama inherited in 2009 when he took the presidential reins from George W. Bush.

When the conversation turned to jobs Thursday night, Mr. Ryan then got a little personal by bringing up the economic troubles facing Mr. Biden’s hometown of Scranton, Pa., to hammer the president’s record on unemployment.

“You know what the unemployment rate in Scranton is today? It’s about 10 percent,” Mr. Ryan said. “You know what it was the day you guys came in?”

“No,” Mr. Biden said.

“Eight-point-five percent,” Mr. Ryan replied. “That’s how it’s going all around America”

But Mr. Biden angrily dismissed the conclusion, arguing that Mr. Ryan doesn’t read statistics.

“That’s not how it’s going,” he said. “It’s going down.”

Thursday night was the biggest political stage of Mr. Ryan’s life, and it marked the generational faceoff the political world has been waiting for: pitting Mr. Biden, the old liberal bull with decades of experience in the Senate, against Mr. Ryan, the young conservative star.

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