His interruptions were strategic, intended to raise questions about the Republican ticket. When Mr. Ryan attacked the administration’s stimulus program, Mr. Biden pointed out that Mr. Ryan had sent him a letter, requesting money for his Congressional district in Wisconsin.

As soon as the debate was over, Republicans were trying to liken Mr. Biden’s performance to that of Al Gore against George W. Bush in 2000, when unflattering cutaway camera shots caught him sighing and rolling his eyes impatiently as Mr. Bush spoke.

But while the two campaigns awaited the results of “insta-polls” determining a winner and a loser, the key question would not come as quickly: Whether Mr. Biden did enough to help move the Obama campaign beyond the president’s own listless debate performance a week earlier. At one point Mr. Ryan even made reference to his imperative to do so, telling him, “I know you’re under a lot of duress to make up for lost ground.”

It was the biggest moment of the campaign for Mr. Ryan, who invigorated the Republican base in August when Mr. Romney asked him to join the ticket. But his role as chairman of the House Budget Committee also opened him up to significant criticism from Mr. Biden, particularly when Mr. Ryan promised a bipartisanship that he said Mr. Obama and Mr. Biden had not delivered as promised.

Before the debate, Democrats were curious about whether Mr. Ryan would stand by his approach to Medicare, which has included different versions of a plan to offer people 65 and older an option to use government subsidies to purchase private insurance. He did, and then some, saying his only intention — and Mr. Romney’s — was to ensure the program’s longevity.

“Medicare and Social Security did so much for my own family,” Mr. Ryan said. “We are not going to jeopardize this program, but we have to save it.”

Looking into the camera, Mr. Biden said, “These guys haven’t been big on Medicare from the beginning,” asking the audience bluntly, “Who do you trust on this?” To Mr. Ryan, he said, “You are jeopardizing this program.”