In Biden's Debate, Aides See Inspiration but Don't Expect Imitation John Gress/Reuters Vice President Joseph R. Biden Jr. and Representative Paul D. Ryan met Thursday night for their only debate of the campaign. WASHINGTON - Vice President Joseph R. Biden Jr."s smirking, aggressive performance during the vice-presidential debate on Thursday could be seen as a message for his boss: Here's how you do it. But for President Obama, who is hunkering down at debate camp in Williamsburg, Va., for the weekend, the challenge is to find the right mix of assertiveness and calm when he faces Mitt Romney on Tuesday in a town hall-style debate. And while Mr. Obama will try to avoid repeating his own passive performance in the first presidential debate, he may also want to steer clear of Mr. Biden's slashing style, which was widely criticized by Republicans as condescending and arrogant. Mr. Obama said late Thursday that his running mate was "terrific" and made a "very strong case" during the debate with Representative Paul D. Ryan, Mr. Romney's running mate. But aides said the president's style would not be affected by Mr. Biden's approach. Mr. Obama will be aggressive next week, they promised, but in his own way. "The president is eager for the next debate, and he'll be passionate and energetic in describing how far we've come as a country in the last four years," said Stephanie Cutter, Mr. Obama's deputy campaign manager. Part of what last night showed is that the facts and the truth matter, and the president will make sure they matter next week as well. Mr. Biden's wide grin and energetic demeanor prompted cheers from Democrats who had been desperate for the kind of in-your-face political rumble that Mr. Obama did not deliver a week ago. But Mr. Biden repeatedly mocked and interrupted Mr. Ryan, leading Republicans to use words like "unhinged," "buffoon" and "disrespectful" in the hours after the fast-paced, 90-minute exchange ended. Mark Salter, a senior adviser to Senator John McCain's presidential campaign in 2008, quipped on his Facebook page: "Evidently, the Obama campaign debate strategy is sleepy cop/crystal meth cop." History suggests that vice-presidential debates have rarely affected elections in big ways. And early snap polls on Friday suggested that most viewers were divided over who won. Still, partisans on both sides seized on Mr. Biden's performance. Jim Messina, the president's campaign manager, said in a statement that Mr. Biden did as well as Democrats had hoped, calling the debate a "clash between facts and conviction on one side and glib lines and empty promises on the other." Chris Lehane, a former senior aide to President Bill Clinton and Vice President Al Gore, said Mr. Biden "came out punching from the first bell and never stopped in his effort to seize back the offensive, especially on the trust issue." He added: "If scored on the basis of the sheer number of punches thrown and punches landed, he won on a TKO." But Tim Miller, a spokesman for the Republican National Committee, helped kick off a drumbeat of Republican criticism, using the hashtag #BidenUnhinged on Twitter. "You almost can't blame Joe Biden for being so unhinged," Mr. Miller said in a statement. It must be frustrating to debate when you have a record that is so hard to defend and not a single tangible plan for the second term besides tax hikes. Sarah Palin, who debated Mr. Biden four years ago as the Republican vice-presidential nominee, said on Fox News that he reminded her of "of watching a musk ox run across the tundra with somebody underfoot." Senator Rand Paul, Republican of Kentucky, told BuzzFeed, an online news site, that Mr. Biden looked like "an arrogant Cheshire cat with a big smile." Mr. Biden may be insulated to some degree from criticism by the mounting demands from Democrats that he make up for Mr. Obama's lethargic display during his debate. If Democrats wanted Mr. Biden to be animated, they certainly got their wish. Hilary Rosen, a Democratic strategist and supporter of Mr. Obama's, said Friday morning that Mr. Biden's unforgiving approach toward his rival motivated the party's core voters. "I think for the base, much of this is theater," Ms. Rosen said in an e-mail. We know who we are for but we need to see great performances because it helps us spread the word that this is a ticket worth buying.