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.