Rep. Bill Alexander (D-Ark.) was the one standing by the door with the red carnation in his lapel. And he wasn't wearing a name tag.

Most of the nearly 500 other people in the Rayburn Building banquet room last night at Alexander's reception, thrown to "Welcome Back Congressmen," had slapped felt-tip-pen-inscribed badges on their chests. Many of the typed name tags intended for the congressmen were left on a table in the hallway.

Stationed by the double doors during most of the party, Alexander greeted each person, from staffer to lobbyist, with a "welcome back." Guests stood by either of two long tables spread with hot and cold hors d'oeuvres, or near one of four bars placed in the corners, as congressmen caught up on news with their colleagues and discussed the holidays.

"Hi!" said Rep. Bernard J. Dwyer (D-N.J.), grabbing the outstretched hand of Rep. Jack Hightower (D-Tex.). "How was home?"

"Well . . . there's gonna be a whole lot of hard work ahead," Hightower answered, adding a somber note. "I mean it. I'm serious."

William Fulbright, former Democratic senator from Arkansas, offered his forecast for President Reagan and the year ahead, as a combo in the middle of the room played the Washington favorite, "New York, New York," more than once.

"He'll have a harder time this year," Fulbright said. "Many of his proposals haven't had much success."

And the congressmen representing East to West, although vastly outnumbered by staffers, lobbyists, lawyers, family and press, seemed to share Fulbright's feelings.

Rep. George Danielson (D-Calif.): "It'll be a difficult year because we'll be bottoming out on the economy. The president will realize we've got to raise taxes. It'll be painful but . . ."

Rep. Dwyer: "I would hope the economy would improve, and I like to think life will be better for all of us . . . but I have some reservations."

Rep. Roy Dyson (D-Md.): "Everyone's in an anticipatory mood, I think. He President Reagan is a tremendous communicator. He can almost have people believe in miracles. But that miracle worker is going to have to get to work."