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Party tensions were briefly cast aside during the official afternoon swearing-in ceremonies, where smiles, applause and handshakes were the order of the day.

Sen. John Thune, South Dakota Republican, walked alongside former Sen. Tom Daschle, the Democrat he unseated in 2004. Sen. John Kerry, Massachusetts Democrat, watched a portion of the event from a seat in the Republican side of the aisle so he could chat with Sen. Richard G. Lugar of Indiana and retiring Sen. John W. Warner of Virginia.

Vice President Dick Cheney, who as Senate president administered the oath of office to senators in groups of four, shook hands with Vice President-elect Joseph R. Biden Jr., who once described him as “the most dangerous vice president in history.”

Newly minted Sen. Jeanne Shaheen, New Hampshire Democrat, said the euphoria of her first day on the job was tempered by the feeling of incredible responsibility that all senators face.

“It’s a celebratory but also a solemn occasion,” said the former governor, who defeated former Sen. John E. Sununu in the Nov. 4 election. “We are faced with tremendous challenges in this country, and I’m excited about having this opportunity at this historic time.”

Fellow freshman Sen. Mark Udall, Colorado Democrat, said the swearing-in ceremony left him “quivering.”

“I was holding on to my cousin Tom for dear life, and he was to me,” said Mr. Udall, referring to Sen. Tom Udall, New Mexico Democrat, who also was sworn in to the Senate for the first time Tuesday.

Former Sen. Pete V. Domenici, a New Mexico Republican who retired last week after serving six terms, made what could be his final appearance on the chamber floor when he escorted Mr. Udall of New Mexico and Mary L. Landrieu, Louisiana Democrat, to be sworn in.

“It’s not so good to think about doing this very often,” said Mr. Domenici, who said he doesn’t expect to visit the Capitol much in the future. “You can’t keep reminding yourself of being a senator. You’ve got to get out of it.”

In the House, California Democrat Nancy Pelosi was sworn in for a second term as speaker after a rare roll-call vote of the full 435-member chamber. Dozens of children and grandchildren of members were on the floor as the new House was sworn in.

Cardinal Theodore McCarrick, the former cardinal for the Roman Catholic diocese of Washington, offered a prayer for the new Congress to open the House session.

Rep. John D. Dingell, Michigan Democrat and the House’s most senior member, administered the oath to Mrs. Pelosi, who invited the children to the speaker’s rostrum as she took the oath.

Both she and House Minority Leader John A. Boehner, Ohio Republican, promised to pursue a spirit of bipartisanship in the new Congress as they tackle an ambitious agenda laid out by Mr. Obama.

“If Barack Obama extends his hand across the aisle, Republicans will extend ours in return,” Mr. Boehner said.

Mrs. Pelosi said it was “time to join hands, not point fingers,” but said she was determined to move on issues such as aid to the economy, health and education.

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