WASHINGTON  If the meeting between President Bush and President-elect Barack Obama on Monday had the potential for a bit of awkwardness, after a campaign in which Mr. Obama laid many of the nation’s ills at the president’s doorstep, the meeting on Thursday night between Vice President-elect Joseph R. Biden Jr. and Vice President Dick Cheney carried its own challenges.

Mr. Biden, after all, had denounced Mr. Cheney in the heat of the campaign as “the most dangerous vice president we’ve had.”

The meeting, as it happens, was slated to take place under dark and stormy skies.

Mr. Barack Obama, meanwhile, announced from Chicago that he would step down from the Senate on Sunday, allowing him to avoid returning to the Senate to cast a ballot in an expected lame-duck session, should his vote be needed.

He remained at his offices in Chicago, after naming on Wednesday a team with considerable experience in the Clinton administration to lead the transitions in the departments of state, defense and treasury.There were reports that he might travel to Georgia to campaign for Jim Martin, a Democrat facing a runoff for a Senate seat against the Republican incumbent, Saxby Chambliss. Senator John McCain was headed to Georgia on Thursday to campaign for Mr. Chambliss.