It was a bittersweet day for Robert J. Dold, who gamely led the ceremonial final House session of the outgoing Congress on Tuesday. It was his own closing act, as well: Mr. Dold, who was a Republican congressman from Illinois, lost his seat in November to Representative Brad Schneider, a Democrat who also defeated him in 2012.

The halls were bustling with energy as the new Congress streamed in, pressing past Mr. Dold into the cramped chamber as he waited for the elevator, carrying an umbrella against the morning’s drenching rain.

“We’re sorry we’re not going to be able to weigh in more on that because, frankly, I think that’s going to be really important,” Mr. Dold said, looking toward the chamber door.