About 500 Democrats dug into their filet mignon last night, and with that made it clear they want four more years of Jimmy Carter.

The "Support President Carter" dinner at the Hyatt Regency was a barter arrangement. In other words: If you eat this meal, said the Carter/Mondale people, you've gone on record for us.

Which is what former U.N. ambassador Andy Young, Coretta Scott King, former GSA chief Jay Soloman, Connecticut Gov. Ella Grasso, House Majority Leader Jim Wright and lots of mayors, state representatives and county commissioners did.

"I have no one else to support," said Solomon, who resigned under pressure from the administration last year.

In his speech, President Carter became Politician Carter. He emphasized the accomplishments of his three years in office, sprinlking them here and there with the personal victories as well.

"You cannot imagine what a thrill goes through my soul," Carter said, "when I see on television Anwar Sadat steaming through the harbor at Haifa."

A little later, Carter added: "I really enjoyed getting a telephone call from Anwar Sadat after Menachem Begin leaves Egypt. He says, 'You know, Mr. President, we get along just fine. I think that prime minister has really changed.'"

The crowd started to chant "Four more years, four more years" after Vice President Mondale introduced Carter. The record was quickly set straight, however.

"The only thing better than four more years," said the president, well aware that there is still a year left to his term, "is five more years."

There were the keep-'em-guessing jokes:

"Fritz, I expect you to run for reelection; I expect you to be renominated, and if so," Carter told Mondale, "I intend to support you."

And the quick-jab jokes directed at the as-yet-unannounced candidate.

"I asked my momma if I could run," said Carter, "and she said okay. Rosalynn said she'd be willing to spend another four years in the White House."

There was one musician among the herd of politicians, namely Charlie Daniels, of the Charlie Daniels Band. He was easy to spot because he is huge and wears a cowboy hat.

"I just think he's a damn good man," said Daniels of Carter. "Probably the best man to hold office in my lifetime. And that's it. That's the beginning and end of it."

Daniels said that where he comes from, which is Mount Juliet, Tenn., they love Jimmy Carter. "But I haven't really talked to everybody in town," he admitted. "Of course, that wouldn't be too hard to do."

Naturally, there were the predictable Carter staffers in the crowd. Chief of Staff Hamilton Jordan, for instance. "The Cabinet split 7-5 [on whether to support Carter] and I'm here as an observer," joked Jordan, who drank a Coke.

Despite Jordan's drollery, Cabinet members were in abundance. Hud Scretary Moon Landrieu sat next to Solomon, clapped loudly at everything, nudged a reporter triumphantly whenever there was loud applause, and was horrified when a well-meaning waitress asked if she could remove his mostly-eaten artichoke.

"No!" cried Landrieu. "What is this, a Republican dinner? They don't eat much, but Democrats are hungry." And with that, he attacked the heart.

Then there was Treasury Secretary G. William Miller, who was talking fast and furiously to Detroit Mayor Coleman Young about prime interest rates, which Miller has seen jump to 15 percent since he left the Fed chairmanship and took over at Treasury. When a reporter joined the conversation, talk of the prime ceased. Immediately.

"As the mayor was saying," said Miller, "this administration will do whatever is right."

Carter's media whiz Gerald Rafshoon was there too. And is he supporting the president? "I thought I would," said Rafshoon. "He's a hell of a guy."

Also spotted in the smoky dining room was Mayor Marion Barry, who said he's backing the incumbent. "Yes, I'm supporting him," he confirmed. Two days ago, the mayor's press secretary said Barry did not consider the dinner an endorsement of the president.

Missing from the dinner crowd was Chicago Mayor Jane Byrne, who did, however, show up at the White House reception beforehand. What that meant isn't clear.

The crowd included 109 House members and 25 senators, according to a tally offered by Sen. Daniel Inouye (D-Hawaii). Carter's congressional liaison Frank Moore said his office first started inviting them last Friday.

"The Florida [caucus] may have had something to do with the turnout," Moore said, "but I think it's something else. These guys would call back to accept and say 'Frank, you know, something is going on out there.'"

Even if people didn't pay for their dinners, the event was a lot like your standard fund-raiser. Mideast negotiator Robert Strauss, who played master of ceremonies for the evening, told political jokes. "I'm a member of the diplomatic corps," he said, "and I'm damn embarrassed to be with you cheap political types."

Los Angles Mayor Tom Bradley, Grasso and Wright took the podium and threw around Jimmy Carter superlatives

"Never in all my public career have the cities of this country had a better team in the White House," said Bradley.

"He is an action president," said Grasso.

"Never has there been a period where there have been more pieces of legislative initiative," said Wright.

Lynn Cutler of Black Hawk County, Iowa, one of three women speakers on the program, said everybody kidded her later for not taking advantage of her situation to announce her candidacy for Congress. "But I'm going to do that in two weeks."

Hyatt's catering manager, Jospeh Endress, putting the cost of the dinners at $21 each, said the original Carter/Mondale order, made three weeks ago, had been for 400 dinners.

"It must have been the Florida caucus that did it," said Endress. "But it broke my heart when they upped the order to 575. I was planning to serve a seven-course dinner."