Everyone cooed when the little Nicaraguan girl in a flouncy skirt walked up to President Reagan and presented him with a big photograph of Nicaraguan children at last night's fundraiser for refugees who have fled the Sandinista government. Reagan, smiling, knew just what to do.

He picked her up and they both beamed into the cameras. The room filled with waves of applause and cheers as he kissed her.

The party for the newly formed Nicaraguan Refugee Fund came at the beginning of Reagan's push for congressional approval of $14 million to aid Nicaraguan rebels.

"We cannot have the United States walk away from one of the greatest moral challenges in postwar history," he told the crowd of more than 600 at the J.W. Marriott. "I pledge to you that we will do everything we can to win this great struggle.

"Viva Nicaragua Libre!" he finished.

Then they brought out 8-year-old Patricia Guerra, who was dwarfed by the picture she presented with the inscription "Para el Presidente Reagan: Gracias, de los nin os refugiados Nicaraguenses."

"We're trying not to become too political," said Louisiana legislator and dinner cochairman Woody Jenkins.

The Fund's literature, however, condemns the Sandinistas. And last night, the crowd rushed to applaud each time Reagan did the same. A standing ovation followed his comment that ". . . the history of this century forces me to believe . . . that to do nothing in Central America is to give the first communist stronghold on the North American contintent a green light to spread its poison through this free and increasingly democratic hemisphere."

Reagan's visit was unusual. He rarely goes to fundraisers that are not for political candidates, preferring to send letters or videotapes. Near the hotel, about 100 demonstrators carried coffins and chanted, "We say no, we say no, stop the contra money flow." The guests, arriving at the door by car, probably were unaware of the protesters around the corner.

"We recognize Reagan has been distorting the facts of who the contras are, and we don't want to see our tax dollars go towards aid," said protest organizer Laura Worby earlier in the day.

Last night, Reagan introduced lay minister and refugee Bayardo Santaeliz to the diners, who had paid from $250 to $500 to attend. According to the Refugee Fund, Sandinista forces invaded his church during a religious service, tied him up and set the church on fire. Santaeliz, his scarred face in a broad grin, went up to the dais and posed with Reagan.

"You know, I was going to ask all these fellas at the cameras if you couldn't turn them off me and put them on him, but he came up here, so I didn't ask you that," Reagan said. "I think America has to see, America has to see the true face of Nicaragua."

Santaeliz and four other refugees who came to the United States under the auspices of the Fund were shown from table to table during dinner, host families translating their stories to the guests.

"The story with this girl is very sad," said Gustavo Ortiz, an economist with the International Monetary Fund, pointing to the small girl in a white dress and orange arm sling who is staying with his family. "She was shot in her arm . . . Her two brothers were killed."

As often happens with charity events, many of the familiar names that made up the "Dinner Committee" and "Special Dinner Committee" and "Honorary Dinner Commitee" didn't show for the actual dinner. Bob Hope, Jeane Kirkpatrick, Jack Kemp, Nelson Bunker Hunt, J. Peter Grace -- none of them was there. Actors Robert Stack and Hugh O'Brian, and Phyllis Schlafly and CIA Director William Casey did make it, however.

"I'm here solely on behalf of the homeless refugees," said Sen. John Warner (R-Va.) after Reagan left. "That's a very disturbing situation, therefore I offered to come."

As for the fate of the $14 million in contra aid?

"I think it's far too early."

During the predinner reception, True Davis, former ambassador to Switzerland and Refugee Fund chairman of the board, said, "It couldn't be a political event because I'm a conservative Democrat. It's bipartisan -- really. When you get into humanitarian events . . ."

But when asked about how he would respond if Reagan called for aid to the contras during his speech, Davis said, "I would agree with that. I'm very critical of President Carter for the way he eliminated the Somoza government. If you have a government that is working and friendly to the United States, you leave it alone."