President Barack Obama worked the room, strutting from table to table at the congressional luncheon in the Capitol’s ornate Statuary Hall and schmoozing Republicans and Democrats alike.

When he came to a table filled predominantly with House Republicans, his main rivals during his first term, he cut the tension with a joke.

Embracing House Armed Services Chairman Howard “Buck” McKeon, R-Calif., and pointing to Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, the president said, “I hope you know it’s a complete coincidence that we put the chairman of the Joint Chiefs next to the House Armed Services chairman.”

Obama then made his way to Republican Policy Committee Chairman James Lankford of Oklahoma. “I’m hoping to find ways to work together,” Obama told him.

Indeed, the two sides have not yet found the formula to work cooperatively. But if there is ill will, it was set aside Monday, as Obama traveled to the Capitol for his second inauguration, a ritual that fills the Capitol, if only for one day, with pomp rather than partisanship.

Addressing the luncheon, Obama struck a chord of togetherness, telling the congressional leaders, Cabinet secretaries, Supreme Court justices, Presidents Jimmy Carter and Bill Clinton and their families that he is confident they can have an effect for the better.

“I recognize that democracy is not always easy, and I recognize that there are profound differences in this room,” he said. “But I just want to say thank you for your service and thank your families for their service, because regardless of our political persuasions and perspectives, I know that all of us serve because we believe that we can make America [better] for future generations.”

Speaker John A. Boehner of Ohio bestowed on the president and Vice President Joseph R. Biden Jr. two flags that flew over the Capitol on Monday. House Majority Leader Eric Cantor, R-Va., meanwhile, gave the men a pair of crystal vases, one hand-etched with the Capitol, the other with the White House.

The reverence for Obama was bipartisan as well. Rules ranking member Louise M. Slaughter, D-N.Y., and Sen. Roy Blunt, R-Mo., posed for photos with the president. Perhaps the biggest hug was reserved for Sen. Tom Coburn, R-Okla., Obama’s friend from his time in the Senate.

The luncheon went off without a hitch except for one thing — Biden almost did not make it. As his entrance was announced to the room, he was nowhere to be found. Boehner’s staff scrambled to find out where he was, all the while holding back Sens. Debbie Stabenow, D-Mich., and John Thune, R-S.D., from entering the room.

After nearly five minutes of confusion, a Secret Service agent announced that Biden would be coming from Boehner’s office. To the relief of the anxious staff, Biden emerged with Sen. Lamar Alexander, R-Tenn., and was reintroduced to the room.

The inaugural ceremony was nearly flawless. Inauguration attendees who also attended the event four years ago called Monday’s weather balmy compared with the frigid temperatures of 2009. As early morning turned into early afternoon, however, the sun disappeared behind the clouds and those with down jackets and woolen socks were among the fortunate.

Lawmakers were generally dressed either for the occasion or for the elements.

Rep. Debbie Wasserman Schultz, D-Fla., had a fur-trimmed coat, while Rep. Lois Capps, D-Calif., went with slacks, sensible sneakers and a red windbreaker. On the Senate side, John McCain, R-Ariz., sported sunglasses despite the overcast skies. Two Western senators, Democrat Max Baucus of Montana and Republican Orrin G. Hatch of Utah, who serve as their parties’ leaders on the Finance Committee, sported cowboy hats.

As members walked onto the West Terrace platform shortly before 11 a.m., old-timers and newbies alike were relishing the excitement.

With camera phones commonplace, many lawmakers snapped pictures of each other or of the vast crowds lining the National Mall. House Majority Whip Kevin McCarthy, R-Calif., and Minority Whip Steny H. Hoyer, D-Md., took pictures on their phones and compared shots.

Many members, such as Reps. Louie Gohmert, R-Texas, and Jim McGovern, D-Mass., waved emphatically at friends in the seats below. After Obama took the ceremonial oath of office, Sen. Mary L. Landrieu, D-La., waved one glove in the air as the crowd erupted into applause.

Amid celebrities such as actors Nick Cannon and Angela Bassett and musicians Katy Perry, John Mayer and Stevie Wonder, freshman Rep. Joaquin Castro, D-Texas, worked the crowds in the hours leading up to the main event, posing for photos and shaking hands.

The self-professed fans, however, were not uniformly sure who he was. Many mistook him for his twin brother, San Antonio Mayor Julián Castro, who delivered a keynote address at the Democratic National Convention last summer. Rep. Castro was gracious with those who approached him and tried gently to correct those who called him “Mayor Castro” and congratulated him on a “terrific speech” — though sometimes he did not.

After lunch, shortly after 2:30 p.m., a small group of staffers gathered outside the East Front carriage entrance on the House side of the Capitol in anticipation of the start of the inaugural parade.

While Capps and Rep. Ron Barber, D-Ariz., went across the street to enjoy a better view from a patch of sun, House Administration Chairwoman Candice S. Miller, R-Mich., and Rep. John L. Mica, R-Fla., stood in the shade near the south door to watch the pageantry.

Inconspicuous amid the pounding of military drums and the stealth movements of the Secret Service, the Obamas and Bidens were in their cars before anyone from far away could notice they had left.

As the East Front cleared out, Mica, who had been taking camera phone photos, let out a small sigh.

“Show’s over,” he said.

Niels Lesniewski contributed to this report.