President Reagan yesterday used his weekly Saturday radio address to cheer American patriotism and the Christmas spirit as values still alive in the country despite economic problems and the presence of American soldiers in the strife-torn Middle East.

"In spite of everything," Reagan said, "we Americans are still uniquely blessed, not only by the rich bounty of our land, but by a bounty of spirit -- a kind of year-round Christmas spirit -- that still makes our country a beacon of hope in a troubled world."

In the Democratic response, Sen. David L. Boren (Okla.) countered Reagan's happy view of the nation by noting that one in five Americans was unemployed at some point during the year.

"Many more of you," Boren said, "had relatives or friends who were out of work and you may have feared the loss of your own job. Our farmers are in trouble. Our small businesses are hurting. The entire world economy is in a deep recession. I don't mention all these problems on Christmas Day to discourage anyone. We've faced far worse problems than these and we've overcome them."

While saying that he did not want to make his Christmas Day talk into a political diatribe, Boren noted the filibusters and intra-party quarrels among Republicans during the just-completed lame-duck session of Congress.

"I suspect," he said, "that a good many of you listening today were disappointed and perhaps even angry at what happened in Washington . . . . There was name-calling and a near shutdown of the whole federal government . . . . When we have most needed togetherness in the face of serious problems, we have had growing divisiveness."

Boren also painted a picture of increasing friction in the country, saying that the divisions are widening between rich and poor, employed and unemployed, blacks and whites, and different regions of the country.

He said there is a need for these groups, as well as for politicians, to come together to deal with the national budget deficit, unemployment, farm problems and Social Security funding.

"If the poor are asked to contribute to the solution, so must the rich," he said, repeating the Democrats' criticism of the Reagan administration as favoring the rich in its proposals for dealing with national problems.

"Christmas is a season of love," Boren said. "The New Year is a time of hope. I hope that all of us, particularly those of us responsible for governing, can take this opportunity to reflect on what we can accomplish if we work together as a single people with a united goal."

Reagan avoided direct political discussion in his broadcast, couching his message in the language of the letters and Christmas cards he has received. He said each had a message of "love, hope, prayer and patriotism."

The president emphasized the patriotism theme, saying he had received a Christmas card from 12 Marines in Lebanon, where American forces have been stationed since September as part of an international peacekeeping force, and a card from a petty officer aboard the aircraft carrier Enterprise who wrote the president that "Christmas in the Indian Ocean is no fun but it's for a very good cause."

The president read a letter that he said was written in October by Ordnanceman First Class John Mooney, who was on the carrier Midway when it encountered a sinking boat carrying 65 Vietnamese refugees in the South China Sea. As the Americans approached the refugees' boat, Reagan said, reading from the letter, the refugees called out: "Hello America sailor! Hello Freedom Man!"

Reagan said the sailor also wrote: "For all our 'problems' with the price of gas, and not being able to afford a new car or the other creature comforts this year . . . I really don't see a lot of leaky boats heading out of San Diego looking for the Russian ships out there . . . . It reminds us all of what America has always been--a place a man or woman can come to for freedom."

The president concluded by saying that Christmas is "even more special for all of us who number among our gifts the birthright of an American."

The radio broadcast, which the president usually delivers live from the White House, was taped on Christmas Eve.

The Reagans are scheduled to leave Monday on a trip to the West Coast.