When the Senate hosted a lunch for its new members-to-be Tuesday, most of the fresh faces showed up in pairs.

Sens.-elect Elizabeth Warren (D-Mass.) and Tammy Baldwin (D-Wis.) walked arm in arm into the Mike Mansfield Room across from the Senate chamber. Sens.-elect Joe Donnelly (D-Ind.) and Mazie Hirono (D-Hawaii) also arrived together, while Sens.-elect Timothy M. Kaine (D-Va.) and Jeff Flake (R-Ariz.) escorted their wives.

Angus King, the so-far independent senator-elect from Maine, walked in alone — though he may choose a partner soon.

King had said he might wait until after Thanksgiving to pick a party, but senators are holding leadership elections Wednesday, forcing him to make a decision much faster than expected.

“The important thing is that whichever decision I make . . . I don’t consider that building a wall between myself and the other party,” he told reporters Tuesday.

During his two terms as Maine’s independent governor, he said, he worked with both parties on several issues.

In an interview before arriving Monday in Washington, King didn’t rule out joining with Republicans despite the fact that the GOP spent millions on attack ads against him during the campaign to succeed retiring Sen. Olympia J. Snowe (R).

“I’m not ruling it out, I’m not ruling it in,” he said. “I’m not ruling it out with the Democrats one way or the other, either.

“I’ve had people urge me [to] not really talk to either side and not take a committee assignment and plant the flag in the middle of the aisle,” he added. “But I’m not inclined to do that because it makes what I’m doing a stunt.”

Most observers and Senate aides expect King to join with Democrats in part because Majority Leader Harry M. Reid (Nev.) and other Democrats didn’t support members of their party in Maine’s Senate race on the assumption that King would join them next year.

King and the 11 other new senators attended a series of briefings and receptions Tuesday. Sen. Charles E. Schumer (D-N.Y.) warmly greeted several new Democrats and their spouses, at one point turning to the wife of Sen.-elect Chris Murphy (Conn.) to say, “He’s going to love this job.”

Warren dodged reporters several times Tuesday, and as she whisked by journalists with Baldwin, she told her new friend, “Pretend you’re talking to me.”

Sen.-elect Ted Cruz (R-Tex.) held court, saying that he hoped to work with President Obama on fiscal issues “if the president is serious about what he said on the campaign trail” about bringing the parties together.

King mostly ignored reporters’ questions as he roamed the halls. He began the day by visiting the offices of Sen. Susan Collins (R-Maine), where they posed for a bank of cameras. Collins said that she looked forward “to welcoming Angus into the group of centrist senators who actually try to solve problems rather than just score political points.”

Then the two exchanged gifts. Collins gave King a pair of Senate cuff links. He gave her a tea-maker.

“Have you learned that your office is likely in the basement?” Collins asked King as they shook hands. “When I was a freshman senator, you actually had to get to the loading dock to get to my office and get through these slips of plastic and find your way.”

“It’s still the United States Senate,” King replied.