Former secretary of state Edmund Muskie was making his way from the reception room to dinner in the Crystal Room last night at the Sheraton-Carlton, looking slightly bemused at life on the circuit. "We must be pretty big wheels," he said to another black-tied Democrat at his side. "We keep going around in circles."

It was an evening when Robert Strauss handed out cigars to celebrate Bert Lance's birthday, Jimmy Carter pushed his new book and 120 Democratic stalwarts outdid themselves in a lovefest of praise, back-patting and debt-defying feats.

They pulled out their checkbooks and fancy clothes to greet former president Carter and former vice president Walter Mondale there. For $2,500 a couple, they were helping to make a dent in the $1.25 million debt connected with the 1980 Carter-Mondale campaign. A quarter-million dollars was raised last night.

Carter, who has made few visits to Washington since he moved out of the White House, said, "Chuck Manatt told me I had few opportunities to come to speak where Bob Strauss didn't start the program. Well, he promised . . ." Strauss had introduced Carter, who sat at the table, which included Muskie. Carter's wife, Rosalynn, and daughter Amy sat at another table across the dimly lit room. Amy, who started her job as a Senate page this week, wore a black dress and slipped in late to take a seat next to her mother.

Former DNC chairman Robert Strauss, Kentucky Gov. John Y. Brown, former domestic adviser Stuart Eizenstat, former acting OMB director Jim McIntyre Jr., former press secretary Jody Powell and current DNC chairman Charles T. Manatt were among the stogie-smoking crowd who listened to two of their favorite Democrats: Carter and Mondale.

Before Strauss introduced the pair, he took time to pass around two boxes of cigars to the crowd as he wished Lance a happy 51st birthday--though the number in question went unmentioned. A string quartet played the usual tune, while the crowd sang "Happy Birthday," Bert.

"He's a big man," Strauss told the crowd about Lance, "but he's a little weak when he can't find a cigar ."

"We join together to pay respects," said Mondale, as he served the first ball in the Ping-Pong game of praise between the two, "to our president, Jimmy Carter, his wife, Rosalynn, and the finest page they've ever had, Amy Carter." Amy, her reddish hair pulled back, grinned shyly.

"When we snap our fingers, Amy, just come running," Mondale joked and then turned serious.

"This administration is being forced to accept the wisdom of your policies," Mondale said, addressing Carter. "I'm convinced history will move in your direction . . .

"I've had good news and bad news this week. While he was on the West Coast, Carter said if I chose to run for president he'd support me. Then I got the next story: Nixon opposes me. The fact of it is, Mr. Nixon has never liked me," he said to much laughter from the crowd.

When it was his turn, Carter responded after a standing ovation, "Tonight, Fritz, you outdid yourself, and we're old partners again."

Carter flashed his trademark smile to the corners of the room and talked about his book, "Keeping Faith: Memoirs of a President."

"I've had a chance to think back to the exciting times in office," Carter said. "I've typed 1,100 pages, double-spaced on my word processor. And I did it myself.

"Then my editors cut out 250 pages and I retyped it myself."